Lucinda is writing a coordinate proof to show that a diagonal of a parallelogram partitions the parallelogram into two equal areas.

Enter your answers in the boxes to complete Lucinda's proof.

Since KLMN is a parallelogram and a parallelogram's opposite sides are parallel and congruent, the coordinates for M are (4x,__).

In △KMN, the length of the base is ___ and the height is ___. So an expression for the area of △KMN is ___.

In △KLM, the length of the base is 3x and the height is 2y. So an expression for the area of △KLM is ___.

Comparing the area of the two triangles that are formed by a diagonal of the parallelogram shows that a diagonal of a parallelogram partitions the parallelogram into two equal areas.