In parallelogram ABCD, the diagonals AC and BD are drawn. intersecting at point K

In parallelogram ABCD, the diagonals AC and BD are drawn. intersecting at point K, and line EF passing through this point. Prove that AE = CF

Let us prove that triangle AOE is equal to triangle COF.

The angle AOE is equal to the angle COF as the vertical angles formed by the intersection of lines AC and EF. The angle OAE is equal to the angle FCO as criss-crossing angles at the intersection of parallel straight lines BC and AD secant EF.

The parallelogram diagonals at the intersection point are divided in half, AO = CO.

Then, triangle AOE is equal to triangle COF in side and two adjacent corners.

Since the triangles are equal, the segment AE is equal to CF, as required.