Abbreviation for Corresponding Parts Of Congruent Triangles are Congruent
. An important principle used
in plane geometry
for proving that lines or angles are equal. Just prove that they're corresponding parts of congruent
triangles, and let CPCTC do the rest.
Prove: If the bisector of the vertex angle B
of a triangle is perpendicular to ^
the base, it bisects the base. /|\
Given: In Δ ABC, BD bisects angle ABC, /3|4\
BD is perpendicular to AC. / | \
To Prove: AD = DC /__1|2__\
A D C
1. BD bisects angle ABC 1. Given.
2. ∠ 3 = ∠ 4 2. To bisect is to divide into equal parts.
3. BD is perpendicular to AC 3. Given.
4. ∠s 1 and 2 are right angles 4. Perpendicular lines meet at right angles.
5. ∠ 1 = ∠ 2 5. All right angles are equal.
6. BD = BD 6. Identity.
7. Δ ABD is congruent to Δ CBD 7. A-S-A
8. AD = DC 8. CPCTC