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Question

In given figure the diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the side BC. Prove that DF×EF=FB×FA
1008898_aab4d263cc764db092a355845d5220df.png

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Solution

In AFD and BFE, we have

1=2 [Vertically opposite angles]

3=4 [Alternate angles]

So, by AA-criterion of similarity,we have

FBEFDA

FBFD=FEFA

FBDF=FEFA

DF×EF=FB×FA [Hence proved]


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