Q. 11

# ABCD is a parallelogram and E is a point on BC. If the diagonal BD intersects AE at F, prove that AF × FB = EF × FD.

Answer :

Given that, AB DC & AD BC

To Prove: AF × FB = EF × FD

Proof: In ∆DAF & ∆BEF

DAF = BEF [ they are alternate angles]

AFD = EFB [ they are vertically opposite angles]

This implies that ∆DAF ∆BEF by AA-similarity criteria.

Now cross-multiply them,

AF × FB = FD × EF

Hence, proved.

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