# How to partition a quadrilateral into a finite number of equal-area triangles

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 (MO user20491).]

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