In the figure, ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB when produced meet at F, prove that AF = 2AB.

Alan Wright

Alan Wright

Answered question

2023-02-19

In the figure, ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB when produced meet at F, prove that AF = 2AB.

Answer & Explanation

Roy Mcclain

Roy Mcclain

Beginner2023-02-20Added 9 answers

Given: ABCD in ||gm, with E as BC's midpoint. To meet AB produced at F, DE is joined and created.
Proof : In CDE and EBF
D E C = B E F C E = E B D C E = E B F C D E B F E D C = B F A B = B F A F = A B + B F = A B + A B = 2 A B A F = 2 A B

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