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

Asked by  | 17th Nov, 2013, 07:37: PM

Expert Answer:

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.

Answered by  | 17th Nov, 2013, 09:41: PM

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