In a parallelogram ABCD, E and F are the points on AB and CD such that AE=CE. Prove that ED is parallel to BF

Given: ABCD is a parallelogram and AE = CF       ...(1)

To Prove: EDBF

Proof:

Since the opposite sides of the parallelogram are equal.

AB = CD         ... (2)

Subtract (1) from (2):

AB - AE = CD - CF

BE = DF      ... (3)

Also, BE is parallel to DF, therefore BEDF is a parallelogram.

Thus ED is parallel to BF.