In triangle ABC, point E is midpoint AB, point F is midpoint AC, point K is midpoint BC.

In triangle ABC, point E is midpoint AB, point F is midpoint AC, point K is midpoint BC. Prove that triangle BEK = triangle FKC.

Since E and K are the midpoints of the sides AB and BC, respectively, it means that EK is the middle line of the triangle ABC, and therefore EK is equal to half of the AC. FC is also equal to half AC (F is mid-AB). Therefore EK = FC.

K and F are the midpoints of the sides BC and AC, respectively, which means that KF is the middle line of the triangle ABC, KF is equal to half of AB, EB is also equal to half of AB. Consequently, KF = EB.

KS is equal to VK, since point K is the middle of the BC side.

This means that the triangle BEK is equal to the triangle FKC on three sides.