These three segments are called diagonals of the quadrilateral. Theorem Midpoints of the diagonals of a complete quadrilateral lie on a line. Below I give two proofs of the Theorem of Complete Quadrilateral . Before you read further, try playing with the applet. The converse is also true.
Lemma follows by comparing two algebraic sums of the areas involved.
The lemma is used in the first proof of the Theorem of Complete Quadrilateral . The second proof depends on Menelaus' theorem . Therefore, the product on the left is also 1. By the converse of Menelaus' theorem, the points K, L, and M lie on a line. Alexander Bogomolny 2773945 .