1. A quadrilateral can be partitioned into 2 equal-area triangles if and only if one diagonal divides equally the other diagonal.
2. It can be proved that most quadrilaterals cannot be partitioned into 3 equal-area triangles.
3. Conjecture: For any natural number $n$, there exists a quadrilateral that cannot be partitioned into $n$ equal-area triangles.


How can one prove this?


[Original question by [bo.gu](https://mathoverflow.net/users/20491/bo-gu) (MO user20491).]



How to partition a quadrilateral into a finite number of equal-area triangles
See [this Wikipedia article.](http://en.wikipedia.org/wiki/Equidissection)


