Systemic thinking about cancer

WEBVTT
Kind: captions
Language: en

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SALMAN KHAN: This is Sal here.

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And I have Dr. David
Agus visiting the office.

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And I want you to
introduce yourself

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because you have kind
of an interesting life.

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DAVID AGUS: Interesting
life is scary.

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But I'm a professor of
medicine and engineering

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at the University of
Southern California.

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I treat cancer patients.

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And I have a lab that looks
at new ways and technologies

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to understand and treat cancer.

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SALMAN KHAN: And that's what's
really interesting, the fact

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that you're a professor of
both medicine and engineering.

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And I guess that's
kind of what we're

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going to touch on
a little bit here.

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DAVID AGUS: Yeah.

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SALMAN KHAN: And so this is
clearly a picture of eggs.

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Why are we looking at eggs?

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DAVID AGUS: Well, if
I gave you those eggs,

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and I put them in your
office, and I say come back

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in three weeks,
what would you have?

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SALMAN KHAN: They would go bad.

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I'm not putting them in
a fridge, I'm assuming.

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I'm just--

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DAVID AGUS: You'd
have a rotten egg.

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Exactly.

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But if I was clever and
I changed the temperature

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in your office to 99.5%
degrees Fahrenheit

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and I rotated those
eggs three times,

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it has to be an odd number,
then at the end of three weeks,

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I'd have a chicken.

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SALMAN KHAN: So that's
what this other picture is.

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You'd have this.

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So you could either
have a rotten egg,

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so this kind of crazy
mess, smelly thing, or you

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have this cute,
adorable chicken.

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DAVID AGUS: Although
they call babies, chicks.

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SALMAN KHAN: Chicks, or chick.

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Yes.

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DAVID AGUS: Yes.

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So a small change in
temperature and gravity

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goes from chaos to order.

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SALMAN KHAN: Right.

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Right.

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DAVID AGUS: And so
we're going to talk

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in a minute about cancer
and all the chaos that's

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involved with it.

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But realize that
that egg, I changed

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the temperature and the gravity
and I went from chaos to order.

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So while will it seem
incomprehensible and unable

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to model cancer,
you're going to start

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to see little changes
can have a major effects.

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SALMAN KHAN: I see.

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And this is what's a
little bit unintuitive.

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So when think about
things like cancer,

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I mean cancer is
not the only one,

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we imagine that we just have
to kind of-- we have to kill it

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or we just have to kind
of have to take it out.

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But what are saying
is, hey, maybe there's

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these subtle things, analogous
to rotating an egg three times

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and getting the
temperature just right,

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that can make it automatically
do different things.

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DAVID AGUS: Exactly.

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To me, cancer is a
verb, not a noun.

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So you're "cancering"--

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SALMAN KHAN: Cancering.

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DAVID AGUS: --when
you have cancer.

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It's not that you have
cancer, you're cancering.

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And so my goal is to change
your state of your body

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from a cancering to a healthing.

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And so the first question is
how do you quantity the state?

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How do we say who
and what you are?

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And so technology is
giving us the opportunity

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to do that as we go forward.

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SALMAN KHAN: Right.

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I just want to get my head
around that because you never

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hear that word "cancering."

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I think you probably invented
that word, [INAUDIBLE],

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or healthing.

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Once again, when
I imagine cancer,

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I think this is the way
most researchers think

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about cancers, is
the set of cells

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that have just gone berserk.

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And you have to remove them or
kill them somehow or stop them

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from spreading.

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And what you're
saying is, no, there's

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something going on systemically
in your body that is cancering.

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It's allowing the
cancer to thrive.

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DAVID AGUS: That's it.

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So your first
definition of something

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you have to cut out, a different
organism, that's bacteria.

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SALMAN KHAN: Right.

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DAVID AGUS: That's an infection.

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So if something from the
outside comes inside of you,

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I give you the
right antibiotic, it

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doesn't care if you're a man
or a woman, you're six feet

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or you're three feet,
if that antibiotic

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targets the bacteria,
it goes away.

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The difference in cancer,
it's your own cells

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that have gone a
little bit crazy.

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And so we have to
change the interaction

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of the body and
the cells in order

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to make that patient better.

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Very different than something
without, this is within.

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SALMAN KHAN: I see.

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In other words, I'm
just-- it's fascinating

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because there's all sorts
of parallels in, I guess,

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everyday life, depending
on what you believe.

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But some people, if
there's crime in an area,

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there's one point of view
that you need to police it.

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You have to arrest
all the criminals.

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But then, hey,
maybe the criminals

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keep coming because there's
certain environmental factors.

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Maybe there's just
a lot of poverty

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and there's lack of education.

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And so you're saying, hey,
let's look at the things

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systemically, as
opposed to just--

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DAVID AGUS: Hunting.

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Put some lights in the area,
put some police driving by.

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But all of a sudden, the
crime level goes down.

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SALMAN KHAN: Right.

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Right.

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It's not just about
arresting the criminals.

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DAVID AGUS: Exactly.

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SALMAN KHAN: It's about
preventing the crime.

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DAVID AGUS: Let me tell you
about a clinical trial that

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was done a couple years.

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It's the coolest clinical trial.

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And they took women
after optimal therapy

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for breast cancer,
these they were

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women who were
premenopausal, so really

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aggressive breast cancer.

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Half of them, after
treatment, got placebo.

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And half of them got a
drug that builds bone.

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SALMAN KHAN:
Interesting [INAUDIBLE].

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Let me write this down.

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So this is breast cancer.

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So these are people--

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DAVID AGUS: These are young
women with breast cancer.

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SALMAN KHAN: Right.

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Right.

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And half got a placebo, which
means just like a sugar pill.

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DAVID AGUS: Sugar pill.

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SALMAN KHAN: And then
you give that to patients

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just to make them think that
they might-- because sometimes

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the psychological
impact [INAUDIBLE].

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DAVID AGUS: And
this was ethical.

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And it's very important to talk
about whether it was ethical

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or not.

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It was ethical
because they already

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got their treatment
for breast cancer.

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And normally in those
women, we just wait.

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And hopefully, they're cured.

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And we see if it may recur.

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SALMAN KHAN: Right.

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DAVID AGUS: So in those women,
we divided them into half.

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And we gave this pill.

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It was a placebo.

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And half, we give a drug for
osteoporosis that builds bone.

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SALMAN KHAN:
Osteoporosis, osteo--

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DAVID AGUS: You say, why
are you wasting someone

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with breast cancer's
time by giving them

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a drug that targets bone.

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SALMAN KHAN: Right.

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Right.

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Right.

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DAVID AGUS: The reason is breast
cancer metastasizes to bone.

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SALMAN KHAN: And
it metastasizes, it

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spreads to bone.

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DAVID AGUS: It spreads to bone.

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SALMAN KHAN: And that's when
cancer just goes, [INAUDIBLE].

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DAVID AGUS: Right.

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It goes to the bone.

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It likes the bone.

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So the argument, if I change
the soil, the seed won't grow.

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Because remember, when
you have a garden,

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you can give your
fertilizer or make that soil

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so those tomato plants love it.

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SALMAN KHAN: Right,
right, right.

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DAVID AGUS: And so that's
what we're doing here.

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We're making the bone different.

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SALMAN KHAN: Right.

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And so once again,
the system thinking

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is that before, if you have
these breast cancer cells that

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are just growing, the view
is, hey, let's irradiate them.

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Let's slice them out.

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Let's get chemicals that
will be toxic to these cells

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and kill them.

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What you're saying is
cancer really starts

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to become a real
negative once it spreads.

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And what you're saying
is let's keep it

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from spreading maybe where
it's the most common to

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spread, which is in the bone.

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So before the bone
drug, the cancer spread.

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The cancer could kind
of take root in the bone

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and then start spreading
and metastasizing.

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This is what metastasis is.

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DAVID AGUS: Um-huh.

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SALMAN KHAN: And instead,
you're saying maybe

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if you have this special
drugs, this osteoporosis drug,

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it makes the bone that
much stronger and less

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susceptible to
this type of thing.

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And then that won't
be able to happen.

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DAVID AGUS: Exactly.

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SALMAN KHAN: Right.

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Right.

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Fascinating.

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DAVID AGUS: So at the
end of that trial,

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the cancer recurrence
was reduced by 40%.

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SALMAN KHAN: Wow.

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DAVID AGUS: At the end of that
trial, new breast cancer, so

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a separate breast
cancer-- because once

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you have one breast cancer,
you can get another breast

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cancer-- that was down by 35%,

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SALMAN KHAN: Wow.

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DAVID AGUS: So this notion
of changing the system--

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because remember, this is
a drug that didn't even

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touch the breast cancer--
had a dramatic effect

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in the survival of
these young women.

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SALMAN KHAN: Right.

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Right.

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DAVID AGUS: So
again, it just makes

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this a whole new way of
thinking about disease.

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SALMAN KHAN: Right.

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Right.

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So if we were putting
words on things, the way

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that most people think
about disease right now,

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you call it kind of a
reductionist, where they're

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just going to focus on
one narrow part of it.

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They're trying to focus on
this thing right over here.

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And you're advocating for
kind of a more systemic way

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of thinking about
it, where you think

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about everything that
this might involve

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or that might affect it.

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DAVID AGUS: It's so wild is that
for the last several decades,

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we're trying to focus on the
individual cell, and then

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the individual gene, and
then the piece of the gene.

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And we forgot to
take that step back

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and look at the whole system.

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And so remember, the
cancer is your normal cell

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that's gone a little bit crazy.

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So we have to model
that whole system

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and figure out a way to control
it so the cancer won't like it.

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SALMAN KHAN: Wow.

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Fascinating.

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Fascinating.

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And then we have pictures
of what some of these things

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look like.

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So what is this right over here?

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DAVID AGUS: So this is a liver
that's taken out of a patient.

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And the white spots
there are colon cancer

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that's metathesizes,
again spread to the liver.

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SALMAN KHAN: Right.

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So it's a cancer that
grew up in the colon.

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And at some point, it was able
to spread and kind of liberate

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itself and then attach
on to the liver.

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And it's metastasized
to the liver.

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And now, it's kind of growing
in this-- it looks, at least

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from this picture, kind of
a cauliflower-like shape.

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DAVID AGUS: Exactly.

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Exactly.

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And then if I showed this
to a surgeon, or someone who

00:08:01.120 --> 00:08:03.010
normally operates
on livers, they

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would know right away, hey, that
looks like colon cancer gone

00:08:06.070 --> 00:08:06.740
to liver.

00:08:06.740 --> 00:08:07.310
SALMAN KHAN: Right.

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Right.

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SALMAN KHAN: And if you look at
the next picture on the right,

00:08:10.223 --> 00:08:13.390
that's colon cancer inside of a
lymph node under a microscope.

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SALMAN KHAN: And
these are the lymph?

00:08:15.374 --> 00:08:17.040
DAVID AGUS: Those are
the normal lymphs.

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SALMAN KHAN: Lymphs.

00:08:17.530 --> 00:08:18.740
And this right here
is the colon cancer?

00:08:18.740 --> 00:08:19.450
DAVID AGUS: Exactly.

00:08:19.450 --> 00:08:19.790
SALMAN KHAN: OK.

00:08:19.790 --> 00:08:21.490
DAVID AGUS: And so
any pathologist would

00:08:21.490 --> 00:08:24.156
look under a microscope and they
would make a diagnosis and say,

00:08:24.156 --> 00:08:27.500
hey, this looks like colon
cancer gone to the lymph.

00:08:27.500 --> 00:08:29.050
And in the bottom
is a different way

00:08:29.050 --> 00:08:32.030
of looking at cancer,
which is a CAT scan.

00:08:32.030 --> 00:08:34.679
So this is basically a
three-dimensional X-ray.

00:08:34.679 --> 00:08:36.400
I took a slice
right in the middle

00:08:36.400 --> 00:08:40.030
that person's body and those
translucent areas in the middle

00:08:40.030 --> 00:08:42.030
there are colon
cancer metastasis.

00:08:42.030 --> 00:08:42.780
SALMAN KHAN: This?

00:08:42.780 --> 00:08:44.280
DAVID AGUS: Those
darker areas, yes.

00:08:44.280 --> 00:08:45.427
SALMAN KHAN: OK.

00:08:45.427 --> 00:08:47.010
DAVID AGUS: And so
what's amazing is--

00:08:47.010 --> 00:08:47.760
SALMAN KHAN: That's
in their liver.

00:08:47.760 --> 00:08:50.370
DAVID AGUS: Colon cancer looks
a certain way, in a lymph node,

00:08:50.370 --> 00:08:52.600
in the liver, on a CAT scan.

00:08:52.600 --> 00:08:54.650
And it always looks that way.

00:08:54.650 --> 00:08:57.060
The body doesn't care what
the underlying genetics are

00:08:57.060 --> 00:08:59.930
because the genetics are
dramatically different patient,

00:08:59.930 --> 00:09:01.400
to patient, to patient.

00:09:01.400 --> 00:09:02.729
But it always looks the same.

00:09:02.729 --> 00:09:03.520
SALMAN KHAN: I see.

00:09:03.520 --> 00:09:04.970
DAVID AGUS: So
somehow, evolution

00:09:04.970 --> 00:09:08.810
is selecting out for phenotype,
which is what things look like,

00:09:08.810 --> 00:09:10.570
not necessarily for genotype.

00:09:10.570 --> 00:09:11.250
SALMAN KHAN: Which
is their actual--

00:09:11.250 --> 00:09:12.857
the DNA that makes
up what they are.

00:09:12.857 --> 00:09:13.690
DAVID AGUS: Exactly.

00:09:13.690 --> 00:09:15.405
And so we're
focusing on genotype.

00:09:15.405 --> 00:09:17.840
And genotype is very
important and it's

00:09:17.840 --> 00:09:19.970
going to give us some
understanding over time.

00:09:19.970 --> 00:09:22.880
But we have to also
take that step back

00:09:22.880 --> 00:09:25.510
and look at the phenotype, and
look at what it looks like,

00:09:25.510 --> 00:09:28.000
and try to change
those interactions.

00:09:28.000 --> 00:09:30.350
Remember, if a patient
has early cancer,

00:09:30.350 --> 00:09:32.200
we've learned a lot
in the last 10 years.

00:09:32.200 --> 00:09:34.110
So if you have early
cancer, and I cure you

00:09:34.110 --> 00:09:36.960
with surgery, the day
before surgery I can always

00:09:36.960 --> 00:09:38.572
find cancer cells
in the blood,--

00:09:38.572 --> 00:09:39.280
SALMAN KHAN: Wow.

00:09:39.280 --> 00:09:40.950
DAVID AGUS: --even
though you were cured.

00:09:40.950 --> 00:09:42.320
So the old days,
we thought, well,

00:09:42.320 --> 00:09:44.695
you have to wait till it goes
out through our bloodstream

00:09:44.695 --> 00:09:45.860
and gets out there.

00:09:45.860 --> 00:09:47.040
That's wrong.

00:09:47.040 --> 00:09:49.659
It's can it live outside
that original organ?

00:09:49.659 --> 00:09:50.450
SALMAN KHAN: I see.

00:09:50.450 --> 00:09:52.940
So there's someone who's
cured or they're not

00:09:52.940 --> 00:09:54.070
cancering right now.

00:09:54.070 --> 00:09:56.640
And there is actually
cancer in their blood.

00:09:56.640 --> 00:09:59.300
But because they're
healthy now, or healthier,

00:09:59.300 --> 00:10:01.800
or they're healhing, or I guess
however you want to call it,

00:10:01.800 --> 00:10:03.090
that cancer isn't
able to take hold.

00:10:03.090 --> 00:10:03.960
DAVID AGUS: And
those cells, they

00:10:03.960 --> 00:10:05.390
can't live anywhere
but the colon.

00:10:05.390 --> 00:10:05.990
SALMAN KHAN: Fascinating.

00:10:05.990 --> 00:10:07.270
DAVID AGUS: So listen
to this experiment.

00:10:07.270 --> 00:10:08.620
This is the wildest experiment.

00:10:08.620 --> 00:10:09.780
They took a mouse.

00:10:09.780 --> 00:10:12.120
And they took breast
cancer and they put it

00:10:12.120 --> 00:10:14.400
in the left breast
and the right breast.

00:10:14.400 --> 00:10:17.330
And they colored them
red and green, the cells.

00:10:17.330 --> 00:10:19.590
They waited a day,
they went back,

00:10:19.590 --> 00:10:22.130
and the cells were half
red, half green; half red,

00:10:22.130 --> 00:10:23.210
half green.

00:10:23.210 --> 00:10:24.690
Because we always
thought if cancer

00:10:24.690 --> 00:10:27.522
is something in one
local spot, it really

00:10:27.522 --> 00:10:29.730
is a disease that keep going
through the bloodstream.

00:10:29.730 --> 00:10:31.010
And it likes those breasts.

00:10:31.010 --> 00:10:32.720
That's why it keeps
going back there.

00:10:32.720 --> 00:10:33.030
SALMAN KHAN: So interesting.

00:10:33.030 --> 00:10:34.613
And when I always
think of metastases,

00:10:34.613 --> 00:10:36.370
and I can never say
is the word, I always

00:10:36.370 --> 00:10:37.890
imagine it, OK, that's
the cancer that's

00:10:37.890 --> 00:10:39.360
finally gotten to
the lymph network.

00:10:39.360 --> 00:10:41.050
It's finally gotten to the blood
vessels and now it's spreading

00:10:41.050 --> 00:10:42.924
But you're saying that
there's actually often

00:10:42.924 --> 00:10:45.680
cancer that has gotten
to the transportation

00:10:45.680 --> 00:10:46.890
networks of the body.

00:10:46.890 --> 00:10:48.575
But it has still
not metastasized

00:10:48.575 --> 00:10:50.200
because it's not able
to take hold yet.

00:10:50.200 --> 00:10:51.080
DAVID AGUS: Exactly.

00:10:51.080 --> 00:10:51.470
SALMAN KHAN: That's fascinating.

00:10:51.470 --> 00:10:51.880
DAVID AGUS: Exactly.

00:10:51.880 --> 00:10:53.890
And over time, we're going
to get the technology

00:10:53.890 --> 00:10:56.560
to interrogate those cells
to say, hey, this one

00:10:56.560 --> 00:10:57.870
can take hold here.

00:10:57.870 --> 00:11:00.412
Therefore, I have to change
where it would take hold.

00:11:00.412 --> 00:11:02.620
We're just at the beginning
of that technology that's

00:11:02.620 --> 00:11:03.790
going to change everything.

00:11:03.790 --> 00:11:05.331
SALMAN KHAN: And
the reason why we're

00:11:05.331 --> 00:11:07.450
looking at these, the
fact that colon cancer

00:11:07.450 --> 00:11:09.450
starts in the colon and this
is how it looks when it spreads

00:11:09.450 --> 00:11:11.533
to different parts of the
body, what you're saying

00:11:11.533 --> 00:11:16.430
is that we shouldn't maybe
be so fixated on just

00:11:16.430 --> 00:11:19.066
the DNA of colon
cancer because it

00:11:19.066 --> 00:11:21.190
can be very different from
one patient to the next.

00:11:21.190 --> 00:11:23.154
But maybe on kind of
its macrobehavior,

00:11:23.154 --> 00:11:25.070
it's phenotype, how it
looks, and how behaves.

00:11:25.070 --> 00:11:27.980
And that way,
it'll give us clues

00:11:27.980 --> 00:11:29.377
maybe on how we can change it.

00:11:29.377 --> 00:11:30.210
DAVID AGUS: Exactly.

00:11:30.210 --> 00:11:30.910
SALMAN KHAN: Fascinating.

00:11:30.910 --> 00:11:31.430
Thanks a bunch.

00:11:31.430 --> 00:11:32.471
This is very interesting.

00:11:32.471 --> 00:11:33.960
DAVID AGUS: It's great.


Similarity example where same side plays different roles

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:05.120
In this problem, we're asked
to figure out the length of BC.

00:00:05.120 --> 00:00:06.850
We have a bunch
of triangles here,

00:00:06.850 --> 00:00:10.030
and some lengths of sides,
and a couple of right angles.

00:00:10.030 --> 00:00:12.290
And so maybe we can
establish similarity

00:00:12.290 --> 00:00:13.715
between some of the triangles.

00:00:13.715 --> 00:00:16.340
There's actually three different
triangles that I can see here.

00:00:16.340 --> 00:00:19.372
This triangle, this triangle,
and this larger triangle.

00:00:19.372 --> 00:00:21.080
If we can establish
some similarity here,

00:00:21.080 --> 00:00:23.070
maybe we can use
ratios between sides

00:00:23.070 --> 00:00:26.890
somehow to figure
out what BC is.

00:00:26.890 --> 00:00:30.050
So when you look at it, you have
a right angle right over here.

00:00:30.050 --> 00:00:33.150
So in triangle BDC, you
have one right angle.

00:00:33.150 --> 00:00:36.450
In triangle ABC, you
have another right angle.

00:00:36.450 --> 00:00:40.870
If we can show that they have
another corresponding set

00:00:40.870 --> 00:00:42.890
of angles are congruent
to each other,

00:00:42.890 --> 00:00:44.550
then we can show
that they're similar.

00:00:44.550 --> 00:00:49.950
And actually, both of those
triangles, both BDC and ABC,

00:00:49.950 --> 00:00:51.879
both share this angle
right over here.

00:00:51.879 --> 00:00:53.920
So if they share that
angle, then they definitely

00:00:53.920 --> 00:00:55.400
share two angles.

00:00:55.400 --> 00:00:57.550
So they both share that
angle right over there.

00:00:57.550 --> 00:00:59.100
Let me do that in
a different color

00:00:59.100 --> 00:01:02.410
just to make it different
than those right angles.

00:01:02.410 --> 00:01:04.370
They both share
that angle there.

00:01:04.370 --> 00:01:06.680
And so we know that
two triangles that

00:01:06.680 --> 00:01:11.710
have at least two
congruent angles,

00:01:11.710 --> 00:01:14.750
they're going to be
similar triangles.

00:01:14.750 --> 00:01:22.370
So we know that
triangle ABC-- We

00:01:22.370 --> 00:01:25.760
went from the unlabeled angle,
to the yellow right angle,

00:01:25.760 --> 00:01:27.274
to the orange angle.

00:01:27.274 --> 00:01:28.440
So let me write it this way.

00:01:37.600 --> 00:01:38.800
ABC.

00:01:38.800 --> 00:01:40.510
And we want to do
this very carefully

00:01:40.510 --> 00:01:43.550
here because the same
points, or the same vertices,

00:01:43.550 --> 00:01:46.052
might not play the same
role in both triangles.

00:01:46.052 --> 00:01:48.510
So we want to make sure we're
getting the similarity right.

00:01:48.510 --> 00:01:53.080
White vertex to the
90 degree angle vertex

00:01:53.080 --> 00:01:55.160
to the orange vertex.

00:01:55.160 --> 00:01:59.840
That is going to be similar
to triangle-- so which

00:01:59.840 --> 00:02:02.480
is the one that is neither a
right angle-- so we're looking

00:02:02.480 --> 00:02:04.674
at the smaller triangle
right over here.

00:02:04.674 --> 00:02:06.590
Which is the one that
is neither a right angle

00:02:06.590 --> 00:02:07.600
or the orange angle?

00:02:07.600 --> 00:02:09.785
Well it's going to be
vertex B. Vertex B had

00:02:09.785 --> 00:02:12.160
the right angle when you think
about the larger triangle.

00:02:12.160 --> 00:02:14.300
But we haven't thought
about just that little angle

00:02:14.300 --> 00:02:15.500
right over there.

00:02:15.500 --> 00:02:17.460
So we start at
vertex B, then we're

00:02:17.460 --> 00:02:19.140
going to go to the right angle.

00:02:19.140 --> 00:02:24.530
The right angle is
vertex D. And then

00:02:24.530 --> 00:02:28.070
we go to vertex C,
which is in orange.

00:02:28.070 --> 00:02:31.170
So we have shown that
they are similar.

00:02:31.170 --> 00:02:33.820
And now that we know
that they are similar,

00:02:33.820 --> 00:02:37.594
we can attempt to take
ratios between the sides.

00:02:37.594 --> 00:02:38.760
And so let's think about it.

00:02:38.760 --> 00:02:40.520
We know what the
length of AC is.

00:02:40.520 --> 00:02:44.320
AC is going to be equal to 8.

00:02:44.320 --> 00:02:45.740
6 plus 2.

00:02:45.740 --> 00:02:50.680
So we know that AC-- what's
the corresponding side

00:02:50.680 --> 00:02:52.340
on this triangle
right over here?

00:02:52.340 --> 00:02:54.131
So you could literally
look at the letters.

00:02:54.131 --> 00:02:57.800
A and C is going to
correspond to BC.

00:02:57.800 --> 00:03:00.310
The first and the third,
first and the third.

00:03:00.310 --> 00:03:04.180
AC is going to correspond to BC.

00:03:04.180 --> 00:03:06.180
And so this is interesting
because we're already

00:03:06.180 --> 00:03:07.660
involving BC.

00:03:07.660 --> 00:03:10.490
And so what is it
going to correspond to?

00:03:10.490 --> 00:03:16.180
And then if we look at BC
on the larger triangle,

00:03:16.180 --> 00:03:20.080
BC is going to correspond to
what on the smaller triangle?

00:03:20.080 --> 00:03:22.770
It's going to correspond to DC.

00:03:22.770 --> 00:03:24.850
And it's good because
we know what AC, is

00:03:24.850 --> 00:03:26.220
and we know it DC is.

00:03:26.220 --> 00:03:27.860
And so we can solve for BC.

00:03:27.860 --> 00:03:30.410
So I want to take one more
step to show you what we just

00:03:30.410 --> 00:03:32.950
did here, because BC is
playing two different roles.

00:03:32.950 --> 00:03:34.710
On this first statement
right over here,

00:03:34.710 --> 00:03:35.670
we're thinking of BC.

00:03:38.280 --> 00:03:41.240
BC on our smaller
triangle corresponds

00:03:41.240 --> 00:03:43.790
to AC on our larger triangle.

00:03:43.790 --> 00:03:45.560
And then in the
second statement,

00:03:45.560 --> 00:03:48.860
BC on our larger
triangle corresponds

00:03:48.860 --> 00:03:51.840
to DC on our smaller triangle.

00:03:51.840 --> 00:03:53.670
So in both of these cases.

00:03:53.670 --> 00:03:56.480
So these are larger
triangles and then

00:03:56.480 --> 00:03:59.920
this is from the smaller
triangle right over here.

00:03:59.920 --> 00:04:01.640
Corresponding sides.

00:04:01.640 --> 00:04:03.510
And this is a cool
problem because BC

00:04:03.510 --> 00:04:07.530
plays two different
roles in both triangles.

00:04:07.530 --> 00:04:09.690
But now we have enough
information to solve for BC.

00:04:09.690 --> 00:04:17.360
We know that AC is equal to 8.

00:04:17.360 --> 00:04:18.750
6 plus 2 is 8.

00:04:18.750 --> 00:04:20.610
And we know the
DC is equal to 2.

00:04:20.610 --> 00:04:21.660
That's given.

00:04:21.660 --> 00:04:23.390
And now we can cross multiply.

00:04:23.390 --> 00:04:27.360
8 times 2 is 16 is
equal to BC times BC--

00:04:27.360 --> 00:04:30.370
is equal to BC squared.

00:04:30.370 --> 00:04:33.650
And so BC is going to be equal
to the principal root of 16,

00:04:33.650 --> 00:04:34.960
which is 4.

00:04:34.960 --> 00:04:39.930
BC is equal to 4.

00:04:39.930 --> 00:04:40.610
And we're done.

00:04:40.610 --> 00:04:42.340
And the hardest part
about this problem

00:04:42.340 --> 00:04:45.200
is just realizing that BC
plays two different roles

00:04:45.200 --> 00:04:49.214
and just keeping your
head straight on those two

00:04:49.214 --> 00:04:49.880
different roles.

00:04:49.880 --> 00:04:51.630
And just to make it
clear, let me actually

00:04:51.630 --> 00:04:53.490
draw these two
triangles separately.

00:04:53.490 --> 00:04:56.935
So if I drew ABC separately,
it would look like this.

00:04:59.700 --> 00:05:02.090
So this is my triangle, ABC.

00:05:05.370 --> 00:05:07.680
And then this is a right angle.

00:05:07.680 --> 00:05:10.490
This is our orange angle.

00:05:10.490 --> 00:05:13.187
We know the length of this
side right over here is 8.

00:05:13.187 --> 00:05:15.770
And we know that the length of
this side, which we figured out

00:05:15.770 --> 00:05:17.730
through this problem is 4.

00:05:17.730 --> 00:05:22.010
Then if we wanted to draw BDC,
we would draw it like this.

00:05:22.010 --> 00:05:27.780
So BDC looks like this.

00:05:27.780 --> 00:05:31.340
So this is BDC.

00:05:31.340 --> 00:05:33.080
That's a little bit
easier to visualize

00:05:33.080 --> 00:05:35.660
because we've already--
This is our right angle.

00:05:35.660 --> 00:05:37.940
This is our orange angle.

00:05:37.940 --> 00:05:42.550
And this is 4, and this
right over here is 2.

00:05:42.550 --> 00:05:43.930
And I did it this
way to show you

00:05:43.930 --> 00:05:47.660
that you have to flip this
triangle over and rotate it

00:05:47.660 --> 00:05:50.294
just to have a
similar orientation.

00:05:50.294 --> 00:05:52.460
And then it might make it
look a little bit clearer.

00:05:52.460 --> 00:05:54.050
So if you found
this part confusing,

00:05:54.050 --> 00:05:57.750
I encourage you to try to flip
and rotate BDC in such a way

00:05:57.750 --> 00:06:00.620
that it seems to
look a lot like ABC.

00:06:00.620 --> 00:06:02.250
And then this ratio
should hopefully

00:06:02.250 --> 00:06:04.620
make a lot more sense.


Challenging similarity problem

WEBVTT
Kind: captions
Language: en

00:00:00.620 --> 00:00:03.780
So given this diagram,
we need to figure out

00:00:03.780 --> 00:00:06.910
what the length of CF
right over here is.

00:00:06.910 --> 00:00:08.910
And you might already
guess that this

00:00:08.910 --> 00:00:11.560
will have to do something
with similar triangles,

00:00:11.560 --> 00:00:18.190
because at least it looks that
triangle CFE is similar to ABE.

00:00:18.190 --> 00:00:21.119
And the intuition there is it's
kind of embedded inside of it,

00:00:21.119 --> 00:00:22.910
and we're going to
prove that to ourselves.

00:00:22.910 --> 00:00:26.460
And it also looks
like triangle CFB

00:00:26.460 --> 00:00:29.509
is going to be similar
to triangle DEB,

00:00:29.509 --> 00:00:31.800
but once again, we're going
to prove that to ourselves.

00:00:31.800 --> 00:00:34.030
And then maybe we can
deal with all the ratios

00:00:34.030 --> 00:00:36.340
of the different sides
to CF right over here

00:00:36.340 --> 00:00:40.590
and then actually figure
out what CF is going to be.

00:00:40.590 --> 00:00:43.220
So first, let's prove to
ourselves that these definitely

00:00:43.220 --> 00:00:44.600
are similar triangles.

00:00:44.600 --> 00:00:47.020
So you have this
90-degree angle in ABE,

00:00:47.020 --> 00:00:50.790
and then you have this
90-degree angle in CFE.

00:00:50.790 --> 00:00:54.620
If we can prove just one
other angle or one other set

00:00:54.620 --> 00:00:57.430
of corresponding angles
is congruent in both,

00:00:57.430 --> 00:00:59.120
then we've proved
that they're similar.

00:00:59.120 --> 00:01:02.800
And there we can either show
that, look, they both share

00:01:02.800 --> 00:01:04.420
this angle right over here.

00:01:04.420 --> 00:01:08.672
Angle CEF is the
same as angle AEB.

00:01:08.672 --> 00:01:12.650
So we've shown two corresponding
angles in these triangles.

00:01:12.650 --> 00:01:14.650
This is an angle
in both triangles.

00:01:14.650 --> 00:01:16.510
They are congruent,
so the triangles

00:01:16.510 --> 00:01:17.610
are going to be similar.

00:01:17.610 --> 00:01:20.190
You can also show that this
line is parallel to this line,

00:01:20.190 --> 00:01:22.330
because obviously these
two angles are the same.

00:01:22.330 --> 00:01:24.824
And so these angles
will also be the same.

00:01:24.824 --> 00:01:26.490
So they're definitely
similar triangles,

00:01:26.490 --> 00:01:27.860
so let's just write that down.

00:01:27.860 --> 00:01:29.090
Get that out of the way.

00:01:29.090 --> 00:01:38.150
We know that triangle ABE
is similar to triangle CFE.

00:01:38.150 --> 00:01:40.800
And you want to make sure you
get it in the right order.

00:01:40.800 --> 00:01:42.630
F is where the
90-degree angle is.

00:01:42.630 --> 00:01:44.260
B is where the
90-degree angle is,

00:01:44.260 --> 00:01:46.680
and then E is where
this orange angle is.

00:01:46.680 --> 00:01:48.090
So CFE.

00:01:48.090 --> 00:01:51.751
It's similar to triangle CFE.

00:01:51.751 --> 00:01:54.250
Now let's see if we can figure
out that same statement going

00:01:54.250 --> 00:01:57.470
the other way, looking
at triangle DEB.

00:01:57.470 --> 00:02:02.147
So once again, you have
a 90-degree angle here.

00:02:02.147 --> 00:02:03.730
If this is 90, then
this is definitely

00:02:03.730 --> 00:02:05.170
going to be 90, as well.

00:02:05.170 --> 00:02:07.870
You have a 90-degree
angle here at CFB.

00:02:07.870 --> 00:02:11.560
You have a 90-degree
angle at DEF or DEB,

00:02:11.560 --> 00:02:13.070
however you want to call it.

00:02:13.070 --> 00:02:15.615
So they have one set
of corresponding angles

00:02:15.615 --> 00:02:17.550
that are congruent,
and then you'll

00:02:17.550 --> 00:02:20.930
also see that they both share
this angle right over here

00:02:20.930 --> 00:02:22.270
on the smaller triangle.

00:02:22.270 --> 00:02:25.420
So I'm now looking at this
triangle right over here,

00:02:25.420 --> 00:02:27.120
as opposed to the
one on the right.

00:02:27.120 --> 00:02:31.510
So they both share this
angle right over here.

00:02:31.510 --> 00:02:35.710
Angle DBE is the
same as angle CBF.

00:02:35.710 --> 00:02:38.080
So I've shown you
already that we

00:02:38.080 --> 00:02:42.080
have this angle is
congruent to this angle,

00:02:42.080 --> 00:02:44.420
and we have this angle
is a part of both.

00:02:44.420 --> 00:02:46.940
So it's obviously
congruent to itself.

00:02:46.940 --> 00:02:49.620
So we have two
corresponding angles

00:02:49.620 --> 00:02:51.350
that are congruent
to each other.

00:02:51.350 --> 00:02:54.330
So we know that this
larger triangle over here

00:02:54.330 --> 00:02:57.740
is similar to this smaller
triangle over there.

00:02:57.740 --> 00:03:00.260
So let me write this down.

00:03:00.260 --> 00:03:02.820
Scroll over to the
right a little bit.

00:03:02.820 --> 00:03:13.510
We also know that triangle DEB
is similar to triangle CFB.

00:03:18.960 --> 00:03:20.382
Now, what can we do from here?

00:03:20.382 --> 00:03:22.590
Well, we know that the ratios
of corresponding sides,

00:03:22.590 --> 00:03:24.960
for each of those
similar triangles,

00:03:24.960 --> 00:03:26.690
they're going to
have to be the same.

00:03:26.690 --> 00:03:29.840
But we only have one side
of one of the triangles.

00:03:29.840 --> 00:03:33.180
So in the case of ABE and CFE,
we've only been given one side.

00:03:33.180 --> 00:03:35.170
In the case of
DEB and CFB, we've

00:03:35.170 --> 00:03:37.140
only been given one
side right over here,

00:03:37.140 --> 00:03:40.176
so there doesn't seem to
be a lot to work with.

00:03:40.176 --> 00:03:42.300
And this is why this is a
slightly more challenging

00:03:42.300 --> 00:03:42.930
problem here.

00:03:42.930 --> 00:03:46.635
Let's just go ahead and see if
we can assume one of the sides,

00:03:46.635 --> 00:03:48.010
and actually,
maybe a side that's

00:03:48.010 --> 00:03:50.660
shared by both of
these larger triangles.

00:03:50.660 --> 00:03:53.320
And then maybe things
will work out from there.

00:03:53.320 --> 00:03:55.660
So let's just assume that
this length right over here--

00:03:55.660 --> 00:03:59.300
let's just assume
that BE is equal to y.

00:03:59.300 --> 00:04:00.790
So let me just write this down.

00:04:00.790 --> 00:04:03.980
This whole length is
going to be equal to y,

00:04:03.980 --> 00:04:06.350
because this at least gives
us something to work with.

00:04:06.350 --> 00:04:11.080
And y is shared by both ABE
and DEB, so that seems useful.

00:04:11.080 --> 00:04:16.120
And then we're going to have
to think about the smaller

00:04:16.120 --> 00:04:17.740
triangles right over there.

00:04:17.740 --> 00:04:22.690
So maybe we'll call BF x.

00:04:22.690 --> 00:04:24.490
Let's call BF x.

00:04:24.490 --> 00:04:26.635
And then let's
FE-- well, if this

00:04:26.635 --> 00:04:28.320
is x, then this is y minus x.

00:04:28.320 --> 00:04:32.320
So we've introduced a
bunch of variables here.

00:04:32.320 --> 00:04:34.800
But maybe with all the
proportionalities and things

00:04:34.800 --> 00:04:36.654
maybe, just maybe,
things will work out.

00:04:36.654 --> 00:04:38.570
Or at least we'll have
a little bit more sense

00:04:38.570 --> 00:04:41.750
of where we can go with
this actual problem.

00:04:41.750 --> 00:04:46.210
But now we can start dealing
with the similar triangles.

00:04:46.210 --> 00:04:50.590
For example, so we want
to figure out what CF is.

00:04:50.590 --> 00:04:53.130
We now know that for these
two triangles right here,

00:04:53.130 --> 00:04:56.300
the ratio of the corresponding
sides are going to be constant.

00:04:56.300 --> 00:04:59.620
So for example, the
ratio between CF and 9,

00:04:59.620 --> 00:05:04.140
their corresponding
sides, has got

00:05:04.140 --> 00:05:08.220
to be equal to the
ratio between y

00:05:08.220 --> 00:05:13.620
minus x-- that's that
side right there--

00:05:13.620 --> 00:05:15.706
and the corresponding side
of the larger triangle.

00:05:15.706 --> 00:05:17.830
Well, the corresponding
side of the larger triangle

00:05:17.830 --> 00:05:20.880
is this entire length.

00:05:20.880 --> 00:05:24.330
And that entire length
right over there is y.

00:05:24.330 --> 00:05:27.440
So it's equal to
y minus x over y.

00:05:27.440 --> 00:05:29.416
So we could simplify
this a little bit.

00:05:29.416 --> 00:05:30.790
Well, I'll hold
off for a second.

00:05:30.790 --> 00:05:32.456
Let's see if we can
do something similar

00:05:32.456 --> 00:05:33.910
with this thing on the right.

00:05:33.910 --> 00:05:39.320
So once again, we have CF,
its corresponding side on DEB.

00:05:39.320 --> 00:05:42.370
So now we're looking at
the triangle CFB, not

00:05:42.370 --> 00:05:44.730
looking at triangle CFE anymore.

00:05:44.730 --> 00:05:46.530
So now when we're
looking at this triangle,

00:05:46.530 --> 00:05:48.556
CF corresponds to DE.

00:05:48.556 --> 00:05:59.940
So we have CF over DE is going
to be equal to x-- let me

00:05:59.940 --> 00:06:03.670
do that in a different color.

00:06:03.670 --> 00:06:05.280
I'm using all my colors.

00:06:05.280 --> 00:06:12.490
It's going to be equal to
x over this entire base

00:06:12.490 --> 00:06:15.680
right over here, so this entire
BE, which once again, we know

00:06:15.680 --> 00:06:17.070
is y.

00:06:17.070 --> 00:06:18.681
So over y.

00:06:18.681 --> 00:06:20.430
And now this looks
interesting, because it

00:06:20.430 --> 00:06:23.410
looks like we have
three unknowns.

00:06:23.410 --> 00:06:25.210
Sorry, we know
what DE is already.

00:06:25.210 --> 00:06:25.960
This is 12.

00:06:25.960 --> 00:06:28.980
I could have written CF over 12.

00:06:28.980 --> 00:06:31.730
The ratio between
CF and 12 is going

00:06:31.730 --> 00:06:34.920
to be the ratio between x and y.

00:06:34.920 --> 00:06:37.160
So we have three unknowns
and only two equations,

00:06:37.160 --> 00:06:38.866
so it seems hard
to solve at first,

00:06:38.866 --> 00:06:40.740
because there's one
unknown, another unknown,

00:06:40.740 --> 00:06:42.860
another unknown, another
unknown, another unknown,

00:06:42.860 --> 00:06:44.360
and another unknown.

00:06:44.360 --> 00:06:46.560
But it looks like I can
write this right here,

00:06:46.560 --> 00:06:49.010
this expression, in
terms of x over y,

00:06:49.010 --> 00:06:50.510
and then we could
do a substitution.

00:06:50.510 --> 00:06:52.134
So that's why this
was a little tricky.

00:06:52.134 --> 00:06:56.900
So this one right here-- let me
do it in that same green color.

00:06:56.900 --> 00:07:03.650
We can rewrite it as CF over 9
is equal to y minus x over y.

00:07:03.650 --> 00:07:07.190
It's the same thing as
y over y minus x over y,

00:07:07.190 --> 00:07:10.770
or 1 minus x over y.

00:07:10.770 --> 00:07:13.160
All I did is, I essentially,
I guess you could say,

00:07:13.160 --> 00:07:15.810
distributed the 1 over y
times both of these terms.

00:07:15.810 --> 00:07:21.310
So y over y minus x over
y, or 1 minus x minus y.

00:07:21.310 --> 00:07:26.770
And this is useful, because
we already know what x over y

00:07:26.770 --> 00:07:27.670
is equal to.

00:07:27.670 --> 00:07:32.060
We already know that x over
y is equal to CF over 12.

00:07:32.060 --> 00:07:37.250
So this right over here, I can
replace with this, CF over 12.

00:07:37.250 --> 00:07:41.060
So then we get-- this is the
home stretch here-- CF, which

00:07:41.060 --> 00:07:47.220
is what we care about, CF over 9
is equal to 1 minus CF over 12.

00:07:47.220 --> 00:07:49.550
And now we have one
equation with one unknown,

00:07:49.550 --> 00:07:51.820
and we should be able to
solve this right over here.

00:07:51.820 --> 00:07:53.805
So we could add CF
over 12 to both sides,

00:07:53.805 --> 00:08:00.700
so you have CF over 9 plus
CF over 12 is equal to 1.

00:08:00.700 --> 00:08:03.360
We just have to find a
common denominator here,

00:08:03.360 --> 00:08:06.450
and I think 36
will do the trick.

00:08:06.450 --> 00:08:11.490
So 9 times 4 is 36, so if you
have to multiply 9 times 4,

00:08:11.490 --> 00:08:12.880
you have to multiply CF times 4.

00:08:12.880 --> 00:08:15.790
So you have 4CF.

00:08:15.790 --> 00:08:18.830
4CF over 36 is the same
thing as CF over 9,

00:08:18.830 --> 00:08:25.060
and then plus CF over 12 is
the same thing as 3CF over 36.

00:08:25.060 --> 00:08:27.560
And this is going
to be equal to 1.

00:08:27.560 --> 00:08:34.460
And then we are left with
4CF plus 3CF is 7CF over 36

00:08:34.460 --> 00:08:35.900
is equal to 1.

00:08:35.900 --> 00:08:37.760
And then to solve for
CF, we can multiply

00:08:37.760 --> 00:08:41.539
both sides times the
reciprocal of 7 over 36.

00:08:41.539 --> 00:08:44.210
So 36 over 7.

00:08:44.210 --> 00:08:48.160
Multiply both sides
times that, 36 over 7.

00:08:48.160 --> 00:08:50.200
This side, things cancel out.

00:08:50.200 --> 00:08:53.350
And we are left with--
we get our drum roll now.

00:08:56.290 --> 00:08:57.880
So all of this
stuff cancels out.

00:08:57.880 --> 00:09:04.830
CF is equal to 1 times 36
over 7, or just 36 over 7.

00:09:04.830 --> 00:09:06.810
And this was a
pretty cool problem,

00:09:06.810 --> 00:09:09.630
because what it shows you
is if you have two things--

00:09:09.630 --> 00:09:12.350
let's say this thing is some
type of a pole or a stick

00:09:12.350 --> 00:09:15.490
or maybe the wall of a building,
or who knows what it is--

00:09:15.490 --> 00:09:19.630
if this is 9 feet tall or 9
yards tall or 9 meters tall,

00:09:19.630 --> 00:09:21.180
and this over here,
this other one,

00:09:21.180 --> 00:09:25.630
is 12 meters tall or 12 yards or
whatever units you want to use,

00:09:25.630 --> 00:09:29.680
if you were to drape a string
from either of them to the base

00:09:29.680 --> 00:09:32.230
of the other, from the top
of one of them to the base

00:09:32.230 --> 00:09:32.880
of the other--

00:09:32.880 --> 00:09:35.970
regardless of how far
apart these two things

00:09:35.970 --> 00:09:38.060
are going to be-- we just
decided they're y apart.

00:09:38.060 --> 00:09:40.180
Regardless of how
far apart they are,

00:09:40.180 --> 00:09:42.950
the place where those two
strings would intersect

00:09:42.950 --> 00:09:45.990
are going to be 36/7
high, or 5 and 1/7

00:09:45.990 --> 00:09:48.320
high, regardless of
how far they are.

00:09:48.320 --> 00:09:52.760
So I think that was a
pretty cool problem.


Tom Brokaw interviews Sal at Education Nation 2011

WEBVTT
Kind: captions
Language: en

00:00:01.512 --> 00:00:05.810
(previous show ending)

00:00:05.810 --> 00:00:08.415
We hope that you guys will join us a little bit later this afternoon

00:00:08.415 --> 00:00:10.799
for more of our Innovation Challenge.

00:00:10.799 --> 00:00:17.299
We'll see you then, thanks very much. (Applause)

00:00:17.299 --> 00:00:22.978
Tom Brokay: Who says that CBS has got a corner on the Amazing Race?

00:00:22.978 --> 00:00:25.578
We've got our own going on here on Education Nation.

00:00:25.578 --> 00:00:28.661
I'm joined now by Sal Khan, who, in a fact,

00:00:28.661 --> 00:00:32.025
is one of the leading innovators of the country,

00:00:32.025 --> 00:00:34.350
but kind of stumbled into it,

00:00:34.350 --> 00:00:36.675
You were a computer science enthusiast.

00:00:36.675 --> 00:00:37.710
Sal: Yes.

00:00:37.710 --> 00:00:39.893
Tom: You got into the venture capital business.

00:00:39.893 --> 00:00:41.952
But you had a niece across the country

00:00:41.952 --> 00:00:44.011
who was having some difficulties doing her math.

00:00:44.011 --> 00:00:45.076
What happened then?

00:00:45.076 --> 00:00:46.784
Sal: Yes, it was 2004,

00:00:46.784 --> 00:00:48.493
they were visiting me right after my wedding.

00:00:48.493 --> 00:00:52.596
It just turned out.. it came out while we were just talking about it

00:00:52.596 --> 00:00:55.043
that she was getting tracked into a slower math class

00:00:55.043 --> 00:00:57.443
when she was going into 7th grade right after the summer.

00:00:57.443 --> 00:01:00.643
And I talked to her.

00:01:00.643 --> 00:01:02.226
I said "Nadia, you are clearly a bright girl --

00:01:02.226 --> 00:01:03.810
And we share a certain amount of DNA --

00:01:03.810 --> 00:01:06.444
There is no way that you should be tracked into a slower math class."

00:01:06.444 --> 00:01:09.744
And so, she agreed that we would tutor each other,

00:01:09.744 --> 00:01:12.578
or I would tutor her when she went back.

00:01:12.578 --> 00:01:14.876
Tom: Now where was she living and where were you living at the time?

00:01:14.876 --> 00:01:16.762
Sal: She was based in New Orleans,which is where I grew up.

00:01:16.762 --> 00:01:18.778
But I was in Boston at the time.

00:01:18.778 --> 00:01:20.795
And we agreed that she would go home,

00:01:20.811 --> 00:01:23.211
and we would get on a conference cal,l and we'd figure out something.

00:01:23.211 --> 00:01:26.111
I used Yahoo Doodle to tutor her.

00:01:26.111 --> 00:01:28.210
And a couple months later, that worked out.

00:01:28.210 --> 00:01:30.577
Then I started tutoring her brothers, a couple other cousins.

00:01:30.577 --> 00:01:32.211
The whole time, I still had a day job.

00:01:32.211 --> 00:01:37.494
And about a year later,

00:01:37.494 --> 00:01:39.176
it just became hard for me to scale myself:

00:01:39.176 --> 00:01:40.859
I had trouble scheduling with all my different cousins

00:01:40.859 --> 00:01:42.455
and family friends and all the rest

00:01:42.455 --> 00:01:45.329
And I had a buddy who I was talking to over dinner.

00:01:45.329 --> 00:01:49.565
And I said: "You know, I'm really enjoying this tutoring thing that I'm doing after work.

00:01:49.565 --> 00:01:50.383
But it is getting difficult."

00:01:50.383 --> 00:01:53.398
And he said ,"Why don't you just record your lectures and put them on YouTube?"

00:01:53.398 --> 00:01:58.117
And I said; "No, YouTube is for dogs on skateboards.

00:01:58.117 --> 00:02:00.641
It's not for serious mathematics, "

00:02:00.641 --> 00:02:06.565
But I tried it out, and, long story short:

00:02:06.565 --> 00:02:09.078
My cousins said that they liked me better on YouTube than in person.

00:02:09.084 --> 00:02:12.883
And other people did too, and they just kept watching it.

00:02:12.883 --> 00:02:16.682
So, it's about 2.5 million people a month are watching the videos.

00:02:16.682 --> 00:02:19.016
Tom: And you've got about 2200 videos.

00:02:19.016 --> 00:02:22.650
Sal: It is now pushing 2800 videos,

00:02:22.650 --> 00:02:25.584
on everything from basic addition to vector calculus,

00:02:25.584 --> 00:02:27.617
and biology, and chemistry, and whatever else.

00:02:27.617 --> 00:02:29.800
Tom: Is this a commercial enterprise?

00:02:29.800 --> 00:02:33.451
Are you doing this just to keep the country better informed?

00:02:33.451 --> 00:02:38.938
Sal: No.. a lot of my buddies from the very for-profit

00:02:38.938 --> 00:02:41.252
investment world are wondering what happened to Sal.

00:02:41.252 --> 00:02:43.735
But I decided to make it a not-for-profit.

00:02:43.735 --> 00:02:46.468
And the real idea is that the fun of this

00:02:46.468 --> 00:02:48.252
is that it reaches as many students as possible.

00:02:48.252 --> 00:02:51.152
So, when I'm on my deathbed, it would be nice...

00:02:51.152 --> 00:02:53.702
you know in the for-profit realm a big success

00:02:53.702 --> 00:02:56.893
would have been IPO or you get acquired.

00:02:56.893 --> 00:02:59.166
But here the big success is you can reach millions and millions of kids.

00:02:59.166 --> 00:02:59.933
It's pretty exciting.

00:02:59.933 --> 00:03:04.001
Tom: What's the appetite for learning that you're finding from this generation?

00:03:04.001 --> 00:03:06.784
Especially in the difficult sciences like Math,

00:03:06.784 --> 00:03:08.951
because we know that we're behind in this country.

00:03:08.951 --> 00:03:11.108
Sal: You know, the really surprising thing is...

00:03:11.108 --> 00:03:12.485
is my cousins were fairly motivated students,

00:03:12.485 --> 00:03:14.334
they were having trouble but I was helping them.

00:03:14.334 --> 00:03:17.117
And when I made the videos, I assumed that they would be..

00:03:17.117 --> 00:03:19.951
that the appeal would be for people like my cousins

00:03:19.951 --> 00:03:22.334
or maybe people like myself..

00:03:22.334 --> 00:03:24.067
I was a pretty good student when I was in middle school,

00:03:24.067 --> 00:03:24.886
and all the rest.

00:03:24.886 --> 00:03:27.451
But the really big surprise: the letters I get are from students

00:03:27.451 --> 00:03:30.718
who a lot of us would have traditionally labeled as the disengaged students.

00:03:30.718 --> 00:03:33.683
The students who said: "I was about to fail out of Algebra...

00:03:33.683 --> 00:03:35.983
I was about to drop out of High School...

00:03:35.983 --> 00:03:37.718
until I found this type of a resource".

00:03:37.718 --> 00:03:41.899
And the big message to me is that it's actually a much larger group of students

00:03:41.899 --> 00:03:43.390
who really, really want to learn

00:03:43.390 --> 00:03:44.738
and you just have to give them an outlet,

00:03:44.738 --> 00:03:47.331
so they're not frustrated, so they don't feel that they're being talked down to.

00:03:47.331 --> 00:03:51.130
And if you give them that, it's not just the 5-10% students that want to learn,

00:03:51.130 --> 00:03:52.750
it's the 90-95%.

00:03:52.750 --> 00:03:55.787
Tom: Sal, in proceeding panels, as you know,

00:03:55.787 --> 00:04:01.242
we talked a lot about poverty, socio-economic depravation,

00:04:01.242 --> 00:04:03.610
people not having access to the internet.

00:04:03.610 --> 00:04:07.059
So are you talking affectively to those who are privileged

00:04:07.059 --> 00:04:12.617
or, if not elite class, than certainly in the middle to upper middle class?

00:04:12.617 --> 00:04:15.294
Sal: You know, across the board, we've seen...

00:04:15.294 --> 00:04:19.325
Clearly I think the main barrier here is that there is some type of internet connectivity

00:04:19.325 --> 00:04:20.227
that someone needs to do,

00:04:20.227 --> 00:04:21.893
but people are already taking our videos,

00:04:21.893 --> 00:04:23.576
they are being translated into 11 languages,

00:04:23.576 --> 00:04:25.042
they're putting them onto DVDs.

00:04:25.042 --> 00:04:28.176
I've gotten pictures of people using them in rural Africa and rural India.

00:04:28.176 --> 00:04:32.176
So even now, it can be accessed by people anywhere.

00:04:32.176 --> 00:04:35.726
And as we go forward, the cost of technology is just getting cheaper and cheaper

00:04:35.726 --> 00:04:39.007
and I think that there is some healthy skepticism around technology

00:04:39.007 --> 00:04:41.225
in the classroom or technology for learning.

00:04:41.225 --> 00:04:43.043
And I think the reason that I solved these is

00:04:43.043 --> 00:04:44.727
because it was nothing to do with technology.

00:04:44.727 --> 00:04:47.127
And we're hoping that between our videos -

00:04:47.127 --> 00:04:49.035
we then we have a huge software platform -

00:04:49.035 --> 00:04:51.405
to give exercises and feedback to students -

00:04:51.405 --> 00:04:54.543
that that will be a catalyst to really use technology.

00:04:54.543 --> 00:04:59.320
Tom: What's the difference between teaching online and teaching in the classroom?

00:04:59.320 --> 00:05:04.671
Sal: The classroom management is a little bit easier. (laughter)

00:05:04.671 --> 00:05:07.088
No, I say that jokingly, but its true.

00:05:07.088 --> 00:05:10.555
I get a huge luxury that when I make my videos

00:05:10.555 --> 00:05:15.089
I pretend that the students are so enthralled by what I have to say

00:05:15.089 --> 00:05:16.539
that I can just imagine it.

00:05:16.539 --> 00:05:19.906
And what's good about that is that it gives me energy...

00:05:19.906 --> 00:05:22.825
It's much harder to sit in front of a room full of 30 kids

00:05:22.825 --> 00:05:25.482
and you're not sure whether some are getting it,

00:05:25.482 --> 00:05:27.079
some are there, some are here.

00:05:27.079 --> 00:05:30.441
What happens is that.. that energy gets conveyed in the videos

00:05:30.441 --> 00:05:32.354
and when the students watch it, they can pause

00:05:32.354 --> 00:05:33.960
and repeat as many times as they want.

00:05:33.960 --> 00:05:36.706
I just got a letter from a kid who watched one video 30 times

00:05:36.706 --> 00:05:38.489
and it took him 30 times to get the idea.

00:05:38.489 --> 00:05:41.673
And what he said was that there no one on the planet that he could have paid

00:05:41.673 --> 00:05:45.722
to tutor him that constant 30 times without judging him.

00:05:45.722 --> 00:05:47.758
And I think that's what students really like.

00:05:47.758 --> 00:05:51.407
Tom: You do have a non-profit, you're out there in the universe of cyberspace

00:05:51.407 --> 00:05:55.106
but are any of the educational systems in this country

00:05:55.106 --> 00:05:58.357
- the districts - either at the local or state level - coming to you

00:05:58.357 --> 00:06:03.007
and saying 'how can we strengthen the relationship between what we need and what you do?'

00:06:03.007 --> 00:06:07.157
Sal: Yes, we started some pilots last year, just almost on a whim

00:06:07.157 --> 00:06:08.706
and its gotten pretty exciting.

00:06:08.706 --> 00:06:11.724
Some of the local schools in the Bay Area,

00:06:11.724 --> 00:06:14.241
they said: 'what would you do if you could do anything you wanted with a 5th grade classroom?"

00:06:14.241 --> 00:06:16.385
We said that we'd have every student working at their own pace:

00:06:16.385 --> 00:06:19.157
watching videos, doing the self-paced exercises.

00:06:19.157 --> 00:06:21.289
Only moving forward once they'd mastered concepts.

00:06:21.289 --> 00:06:24.426
Right now you get a 'B' or a 'C' on a topic.

00:06:24.426 --> 00:06:25.808
That's fine, you passed,

00:06:25.808 --> 00:06:27.528
even though you don't know 10 or 20% of the material.

00:06:27.528 --> 00:06:28.956
And then you move on to more difficult topics.

00:06:28.956 --> 00:06:31.706
So we are saying everyone at their on pace, master concepts first

00:06:31.706 --> 00:06:34.174
and then what happens to the teachers is that they get all of this data:

00:06:34.174 --> 00:06:36.371
who is working on what, what videos are they watching.

00:06:36.371 --> 00:06:37.556
What exercises are they doing.

00:06:37.556 --> 00:06:41.489
So the teacher no longer has to give these 'one size fits all' lectures.

00:06:41.489 --> 00:06:43.311
The teacher can actually get the data and say:

00:06:43.311 --> 00:06:45.613
"Hey look, Tom's having trouble with negative numbers,

00:06:45.613 --> 00:06:46.797
and everyone else is working at their own pace,

00:06:46.797 --> 00:06:50.950
let me sit down next to Tom and actually have a 1-1 intervention with Tom."

00:06:50.950 --> 00:06:53.454
What we've found in the classrooms has been pretty crazy

00:06:53.454 --> 00:06:58.625
before maybe 10% of the teacher's time was spent on that really deep 1-1 mentorship.

00:06:58.625 --> 00:07:00.239
Now it is 90% of their time.

00:07:00.239 --> 00:07:03.173
So what we consider to be the relevant metric

00:07:03.173 --> 00:07:05.789
which is the student-to-time-with-the-teacher ratio.

00:07:05.789 --> 00:07:06.589
That's gone through the roof.

00:07:06.589 --> 00:07:10.322
Tom: Do people in their 40s and 50s, or my age,

00:07:10.322 --> 00:07:12.324
and I'm a grandparent at this age,

00:07:12.324 --> 00:07:16.472
do we tend to underestimate the passions

00:07:16.472 --> 00:07:20.507
and the almost affinity that young people, now coming of age

00:07:20.507 --> 00:07:22.456
with all this technology around them,

00:07:22.456 --> 00:07:26.682
have for using that technology and the expectation that they have for it?

00:07:26.682 --> 00:07:30.580
Sal: Yeah, it surprised me. I wouldn't have thought,

00:07:30.580 --> 00:07:32.248
when I started this up, I wouldn't have thought,

00:07:32.248 --> 00:07:35.815
that when I made videos on sine and cosine and l'Hopital's rule

00:07:35.815 --> 00:07:37.831
that they would become this 'main stream' thing

00:07:37.831 --> 00:07:39.614
but clearly there's this hunger for it.

00:07:39.614 --> 00:07:42.031
And the surprising thing is that it isn't just the younger generation

00:07:42.031 --> 00:07:44.265
we have 30 year olds, 40 year olds, 50 year olds...

00:07:44.265 --> 00:07:48.651
I got a letter from a grandmother that said it was her life dream to learn calculus -

00:07:48.651 --> 00:07:49.875
who knew?

00:07:49.875 --> 00:07:52.782
And she started working on it, so it is really across generations.

00:07:52.782 --> 00:07:59.465
Tom: Do you compliment what you do online with conventional text books

00:07:59.465 --> 00:08:02.651
or math books or offer references?

00:08:02.651 --> 00:08:04.844
Sal: Well, it is an interesting...

00:08:04.844 --> 00:08:06.127
I think that there will always be a role for books.

00:08:06.127 --> 00:08:08.061
But textbooks right now do two things:

00:08:08.061 --> 00:08:11.443
the text tries to teach you something, it is sometimes hard to read.

00:08:11.443 --> 00:08:14.811
And then the exercise try to give you practice.

00:08:14.811 --> 00:08:19.210
We think that on-demand video is often better than the text

00:08:19.210 --> 00:08:22.277
that you see in a lot of text books and that immediate feedback,

00:08:22.277 --> 00:08:24.244
self-paced learning with data and analytics

00:08:24.244 --> 00:08:25.610
and you get the steps of every problem,

00:08:25.610 --> 00:08:26.859
and it is kind of like a video game.

00:08:26.859 --> 00:08:29.895
That that's better than every other answer in the back of the book.

00:08:29.895 --> 00:08:32.960
So it will be interesting to see what happens to the textbook world.

00:08:32.960 --> 00:08:35.609
Tom: What did you learn, if anything, at this point?

00:08:35.609 --> 00:08:38.427
And I know it is empirical of it probably..

00:08:38.427 --> 00:08:41.509
about whether some of us are hard-wired to do math

00:08:41.509 --> 00:08:45.777
and others of us, like me, are hard-wired to do other things.

00:08:45.777 --> 00:08:47.994
I mean people ask me how I got to be a journalist and I say:

00:08:47.994 --> 00:08:51.360
"Algebra 2". (laughter)

00:08:51.360 --> 00:08:52.444
Sal: That's pretty good.

00:08:52.444 --> 00:08:56.562
No, the amazing thing that we've started seeing in these pilots

00:08:56.562 --> 00:08:59.460
in these classrooms is when you let every kid work at their own pace,

00:08:59.460 --> 00:09:02.210
right when you start off, you do see what we traditionally see:

00:09:02.210 --> 00:09:03.677
some of the kids race ahead

00:09:03.677 --> 00:09:06.561
and those are the kids that we all think will be nuclear physicists and whatever else.

00:09:06.561 --> 00:09:10.110
And some of the kids take a little bit longer on one concept to another

00:09:10.110 --> 00:09:14.745
and in a traditional model, you'd say: those kids are meant to be scientists or engineers.

00:09:14.745 --> 00:09:19.766
These kids .. maybe they'll become journalists - which isn't so bad.

00:09:19.766 --> 00:09:24.599
But what we've seen is that if you let them work at their own pace,

00:09:24.599 --> 00:09:27.382
some of those kids who are spending a little extra time on negative numbers

00:09:27.382 --> 00:09:30.047
or exponents. You give them that extra time

00:09:30.047 --> 00:09:33.432
and as soon at they get that some of them just race ahead.

00:09:33.432 --> 00:09:35.322
And so what we're seeing in our data in the classrooms

00:09:35.322 --> 00:09:39.483
is when we are not grouping kids based on early assessment,

00:09:39.483 --> 00:09:41.415
that every week there is a new leader.

00:09:41.415 --> 00:09:44.782
And some of the kids that two or three weeks ago you'd have said were slow or below average

00:09:44.782 --> 00:09:46.370
a week or two or a month later,

00:09:46.370 --> 00:09:47.873
they're the best kid in the class.

00:09:47.873 --> 00:09:50.232
So what we are seeing is that maybe we're just discounting kids

00:09:50.232 --> 00:09:52.849
too early and we are assessing them at the wrong times.

00:09:52.849 --> 00:09:56.865
And it is kind of a predetermined future if you do it that way.

00:09:56.865 --> 00:10:00.299
Tom: How did we loose our way in this country when it came to science education?

00:10:00.299 --> 00:10:05.015
Tom: How did we loose our way when comes to science education in this country?

00:10:05.015 --> 00:10:09.632
When I was a younger guy, the Russians were beating us into Space

00:10:09.632 --> 00:10:12.181
so a lot of people went into Engineering, went into Sciences.

00:10:12.181 --> 00:10:15.082
The Space Race helped accelerate all of that.

00:10:15.082 --> 00:10:18.815
But then we lost our way, it seems to me, in the last part of the 20th century.

00:10:18.815 --> 00:10:20.901
Sal: You know, I think that it has just been bad branding.

00:10:20.901 --> 00:10:22.999
I think, you know its funny, because Science and Engineering

00:10:22.999 --> 00:10:25.115
are fundamentally creative professions.

00:10:25.115 --> 00:10:27.714
I mean 'engineering', the word 'engineering' is to build things

00:10:27.714 --> 00:10:28.932
that have never been built before.

00:10:28.932 --> 00:10:32.448
And the way it's shown and the way, and all of the hoops

00:10:32.448 --> 00:10:34.082
that you have to jump through in your education,

00:10:34.082 --> 00:10:36.515
make it look like its a non-creative field,

00:10:36.515 --> 00:10:37.566
but when you look at it in the real world,

00:10:37.566 --> 00:10:38.599
it is a very creative field.

00:10:38.599 --> 00:10:41.365
So I think the real thing is to get more kids engaged,

00:10:41.365 --> 00:10:44.651
to show them that 1) the math and science itself is beautiful

00:10:44.651 --> 00:10:46.441
and it tells us more about the universe,

00:10:46.441 --> 00:10:48.632
or as much about the universe, as philosophy or anything else.

00:10:48.632 --> 00:10:51.432
It really is a form of philosophy and not only that,

00:10:51.432 --> 00:10:53.799
but the end point you're going to isn't a boring job.

00:10:53.799 --> 00:10:57.734
It is a creative job, it is redefining what people's experiences are.

00:10:57.734 --> 00:10:59.340
I think that if you do it that way,

00:10:59.340 --> 00:11:00.947
I think that a lot of more people will want to get into it.

00:11:00.947 --> 00:11:04.466
Tom: I take of Cyber Space is the new second 'Big Bang',

00:11:04.466 --> 00:11:06.331
we're creating this new universe our there,

00:11:06.331 --> 00:11:08.890
just like we did with the physical first bang.

00:11:08.890 --> 00:11:10.471
And one of the things that's happening is

00:11:10.471 --> 00:11:12.746
that we're watching all these planets

00:11:12.746 --> 00:11:14.884
which one is going to drift too close to the sun,

00:11:14.884 --> 00:11:17.335
which ones are going to form together and form new lifeforms.

00:11:17.335 --> 00:11:20.403
As you look at your model which has been successful,

00:11:20.403 --> 00:11:22.207
have you already began to think:

00:11:22.207 --> 00:11:25.396
how can we expand that model to other areas?

00:11:25.396 --> 00:11:26.851
Sal: Yeah, we've already thought about it.

00:11:26.851 --> 00:11:29.668
So you know that we have the videos I do right now

00:11:29.668 --> 00:11:31.401
and we have this whole software platform

00:11:31.401 --> 00:11:32.710
and I think the interesting thing is

00:11:32.710 --> 00:11:35.019
we are going to start branching off from mathematics,

00:11:35.019 --> 00:11:38.635
our videos already cover the things in biology and economics and all the rest.

00:11:38.635 --> 00:11:40.160
But our exercise platform:

00:11:40.160 --> 00:11:41.685
try to do economics, physics, chemistry,

00:11:41.685 --> 00:11:44.204
and then start to think about how can we do the humanities?

00:11:44.204 --> 00:11:46.769
How can we give people the basic scaffold of say American History?

00:11:46.769 --> 00:11:49.002
And then I think it would be really interesting to see

00:11:49.002 --> 00:11:50.517
how we can do things like creative writing,

00:11:50.517 --> 00:11:51.832
where people are doing projects

00:11:51.832 --> 00:11:54.655
and maybe they can peer review each others essays and things like that.

00:11:54.655 --> 00:11:56.346
I think that there is a whole universe

00:11:56.346 --> 00:11:58.652
that we are just beginning to explore.

00:11:58.652 --> 00:12:00.219
Tom: Well we look forward to your exploration.

00:12:00.219 --> 00:12:02.852
Sal thank you very much from the Khan Academy.

00:12:02.852 --> 00:12:04.084
Sal: Thank you.

00:12:04.084 --> 00:12:05.453
Tom: And you and I will get together later

00:12:05.453 --> 00:12:08.084
and see if we can improve my math skills. Thank you.


Similarity example problems

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:02.360
In this first problem
over here, we're

00:00:02.360 --> 00:00:06.780
asked to find out the length
of this segment, segment CE.

00:00:06.780 --> 00:00:08.430
And we have these
two parallel lines.

00:00:08.430 --> 00:00:10.440
AB is parallel to DE.

00:00:10.440 --> 00:00:12.770
And then, we have these two
essentially transversals

00:00:12.770 --> 00:00:14.420
that form these two triangles.

00:00:14.420 --> 00:00:15.940
So let's see what
we can do here.

00:00:15.940 --> 00:00:17.850
So the first thing that
might jump out at you

00:00:17.850 --> 00:00:21.080
is that this angle and this
angle are vertical angles.

00:00:21.080 --> 00:00:22.870
So they are going
to be congruent.

00:00:22.870 --> 00:00:24.650
The other thing that
might jump out at you

00:00:24.650 --> 00:00:30.580
is that angle CDE is an
alternate interior angle

00:00:30.580 --> 00:00:31.890
with CBA.

00:00:31.890 --> 00:00:34.444
So we have this transversal
right over here.

00:00:34.444 --> 00:00:36.110
And these are alternate
interior angles,

00:00:36.110 --> 00:00:37.900
and they are going
to be congruent.

00:00:37.900 --> 00:00:40.340
Or you could say that, if you
continue this transversal,

00:00:40.340 --> 00:00:43.924
you would have a corresponding
angle with CDE right up here

00:00:43.924 --> 00:00:45.340
and that this one's
just vertical.

00:00:45.340 --> 00:00:47.440
Either way, this
angle and this angle

00:00:47.440 --> 00:00:48.920
are going to be congruent.

00:00:48.920 --> 00:00:51.180
So we've established that
we have two triangles

00:00:51.180 --> 00:00:55.380
and two of the corresponding
angles are the same.

00:00:55.380 --> 00:00:59.732
And that by itself is enough
to establish similarity.

00:00:59.732 --> 00:01:01.940
We actually could show that
this angle and this angle

00:01:01.940 --> 00:01:04.500
are also congruent by
alternate interior angles,

00:01:04.500 --> 00:01:06.007
but we don't have to.

00:01:06.007 --> 00:01:07.715
So we already know
that they are similar.

00:01:07.715 --> 00:01:09.173
And actually, we
could just say it.

00:01:09.173 --> 00:01:11.130
Just by alternate
interior angles,

00:01:11.130 --> 00:01:12.720
these are also going
to be congruent.

00:01:12.720 --> 00:01:15.630
But we already know enough
to say that they are similar,

00:01:15.630 --> 00:01:17.330
even before doing that.

00:01:17.330 --> 00:01:19.770
So we already know
that triangle--

00:01:19.770 --> 00:01:22.920
I'll color-code
it so that we have

00:01:22.920 --> 00:01:24.470
the same corresponding vertices.

00:01:24.470 --> 00:01:26.750
And that's really important--
to know what angles

00:01:26.750 --> 00:01:28.550
and what sides
correspond to what side

00:01:28.550 --> 00:01:31.750
so that you don't mess up
your, I guess, your ratios

00:01:31.750 --> 00:01:34.830
or so that you do know
what's corresponding to what.

00:01:34.830 --> 00:01:48.000
So we know triangle ABC
is similar to triangle--

00:01:48.000 --> 00:01:52.540
so this vertex A corresponds
to vertex E over here.

00:01:52.540 --> 00:01:56.800
It's similar to vertex E. And
then, vertex B right over here

00:01:56.800 --> 00:02:04.660
corresponds to vertex D. EDC.

00:02:04.660 --> 00:02:06.320
Now, what does that do for us?

00:02:06.320 --> 00:02:09.050
Well, that tells us that the
ratio of corresponding sides

00:02:09.050 --> 00:02:12.080
are going to be the same.

00:02:12.080 --> 00:02:14.140
They're going to be
some constant value.

00:02:14.140 --> 00:02:15.950
So we have corresponding side.

00:02:15.950 --> 00:02:22.110
So the ratio, for example,
the corresponding side for BC

00:02:22.110 --> 00:02:23.520
is going to be DC.

00:02:23.520 --> 00:02:25.200
We can see it in just
the way that we've

00:02:25.200 --> 00:02:26.366
written down the similarity.

00:02:26.366 --> 00:02:30.020
If this is true, then BC is
the corresponding side to DC.

00:02:30.020 --> 00:02:41.310
So we know that the length
of BC over DC right over here

00:02:41.310 --> 00:02:44.090
is going to be equal to
the length of-- well,

00:02:44.090 --> 00:02:46.480
we want to figure
out what CE is.

00:02:46.480 --> 00:02:47.660
That's what we care about.

00:02:47.660 --> 00:02:51.190
And I'm using BC and DC
because we know those values.

00:02:51.190 --> 00:02:55.230
So BC over DC is going
to be equal to-- what's

00:02:55.230 --> 00:02:58.630
the corresponding side to CE?

00:02:58.630 --> 00:03:01.230
The corresponding
side over here is CA.

00:03:01.230 --> 00:03:06.200
It's going to be
equal to CA over CE.

00:03:11.440 --> 00:03:13.270
This is last and the first.

00:03:13.270 --> 00:03:14.440
Last and the first.

00:03:14.440 --> 00:03:16.152
CA over CE.

00:03:16.152 --> 00:03:18.540
And we know what BC is.

00:03:18.540 --> 00:03:22.130
BC right over here is 5.

00:03:22.130 --> 00:03:23.055
We know what DC is.

00:03:23.055 --> 00:03:25.190
It is 3.

00:03:25.190 --> 00:03:28.090
We know what CA or AC
is right over here.

00:03:28.090 --> 00:03:29.700
CA is 4.

00:03:29.700 --> 00:03:33.485
And now, we can
just solve for CE.

00:03:33.485 --> 00:03:36.450
Well, there's multiple ways
that you could think about this.

00:03:36.450 --> 00:03:40.350
You could cross-multiply, which
is really just multiplying

00:03:40.350 --> 00:03:42.430
both sides by both denominators.

00:03:42.430 --> 00:03:46.230
So you get 5 times
the length of CE.

00:03:46.230 --> 00:03:49.750
5 times the length of CE is
equal to 3 times 4, which

00:03:49.750 --> 00:03:51.810
is just going to be equal to 12.

00:03:51.810 --> 00:03:59.280
And then we get CE is
equal to 12 over 5,

00:03:59.280 --> 00:04:03.990
which is the same thing
as 2 and 2/5, or 2.4.

00:04:03.990 --> 00:04:06.700
So this is going
to be 2 and 2/5.

00:04:06.700 --> 00:04:07.730
And we're done.

00:04:07.730 --> 00:04:09.570
We were able to use
similarity to figure out

00:04:09.570 --> 00:04:11.740
this side just
knowing that the ratio

00:04:11.740 --> 00:04:15.830
between the corresponding
sides are going to be the same.

00:04:15.830 --> 00:04:18.300
Now, let's do this
problem right over here.

00:04:18.300 --> 00:04:19.050
Let's do this one.

00:04:19.050 --> 00:04:20.633
Let me draw a little
line here to show

00:04:20.633 --> 00:04:22.400
that this is a
different problem now.

00:04:22.400 --> 00:04:24.240
This is a different problem.

00:04:24.240 --> 00:04:27.700
So in this problem, we need
to figure out what DE is.

00:04:27.700 --> 00:04:32.900
And we, once again, have these
two parallel lines like this.

00:04:32.900 --> 00:04:36.000
And so we know corresponding
angles are congruent.

00:04:36.000 --> 00:04:38.800
So we know that angle is going
to be congruent to that angle

00:04:38.800 --> 00:04:40.840
because you could view
this as a transversal.

00:04:40.840 --> 00:04:46.420
We also know that this
angle right over here

00:04:46.420 --> 00:04:49.290
is going to be congruent to
that angle right over there.

00:04:49.290 --> 00:04:52.340
Once again, corresponding
angles for transversal.

00:04:52.340 --> 00:04:54.120
And also, in both
triangles-- so I'm

00:04:54.120 --> 00:04:58.530
looking at triangle CBD
and triangle CAE-- they

00:04:58.530 --> 00:05:00.560
both share this angle up here.

00:05:04.040 --> 00:05:06.150
Once again, we could have
stopped at two angles,

00:05:06.150 --> 00:05:08.730
but we've actually shown that
all three angles of these two

00:05:08.730 --> 00:05:11.340
triangles, all three of
the corresponding angles,

00:05:11.340 --> 00:05:15.440
are congruent to each other.

00:05:15.440 --> 00:05:17.660
And once again, this is
an important thing to do,

00:05:17.660 --> 00:05:20.399
is to make sure that you
write it in the right order

00:05:20.399 --> 00:05:21.690
when you write your similarity.

00:05:21.690 --> 00:05:34.590
We now know that
triangle CBD is similar--

00:05:34.590 --> 00:05:50.349
not congruent-- it is similar
to triangle CAE, which

00:05:50.349 --> 00:05:52.140
means that the ratio
of corresponding sides

00:05:52.140 --> 00:05:53.790
are going to be constant.

00:05:53.790 --> 00:06:00.460
So we know, for example,
that the ratio between CB

00:06:00.460 --> 00:06:03.000
to CA-- so let's
write this down.

00:06:03.000 --> 00:06:07.810
We know that the
ratio of CB over CA

00:06:07.810 --> 00:06:13.662
is going to be equal to
the ratio of CD over CE.

00:06:17.570 --> 00:06:19.220
And we know what CB is.

00:06:19.220 --> 00:06:21.550
CB over here is 5.

00:06:21.550 --> 00:06:22.559
We know what CA is.

00:06:22.559 --> 00:06:23.850
And we have to be careful here.

00:06:23.850 --> 00:06:24.930
It's not 3.

00:06:24.930 --> 00:06:28.380
CA, this entire side is
going to be 5 plus 3.

00:06:28.380 --> 00:06:30.300
So this is going to be 8.

00:06:30.300 --> 00:06:31.690
And we know what CD is.

00:06:31.690 --> 00:06:33.980
CD is going to be 4.

00:06:33.980 --> 00:06:37.390
And so once again, we
can cross-multiply.

00:06:37.390 --> 00:06:39.020
We have 5CE.

00:06:39.020 --> 00:06:46.370
5 times CE is
equal to 8 times 4.

00:06:46.370 --> 00:06:49.810
8 times 4 is 32.

00:06:49.810 --> 00:06:57.400
And so CE is equal to 32 over 5.

00:06:57.400 --> 00:07:02.590
Or this is another way to
think about that, 6 and 2/5.

00:07:02.590 --> 00:07:05.747
Now, we're not done because
they didn't ask for what CE is.

00:07:05.747 --> 00:07:07.830
They're asking for just
this part right over here.

00:07:07.830 --> 00:07:09.210
They're asking for DE.

00:07:09.210 --> 00:07:12.680
So we know that this entire
length-- CE right over here--

00:07:12.680 --> 00:07:15.500
this is 6 and 2/5.

00:07:15.500 --> 00:07:18.120
And so DE right over
here-- what we actually

00:07:18.120 --> 00:07:19.900
have to figure out--
it's going to be

00:07:19.900 --> 00:07:23.420
this entire length,
6 and 2/5, minus 4,

00:07:23.420 --> 00:07:25.790
minus CD right over here.

00:07:25.790 --> 00:07:29.140
So it's going to be 2 and 2/5.

00:07:29.140 --> 00:07:32.157
6 and 2/5 minus 4
and 2/5 is 2 and 2/5.

00:07:32.157 --> 00:07:32.740
So we're done.

00:07:32.740 --> 00:07:36.850
DE is 2 and 2/5.