ABCD is parallelogram and E is a point on BC. If the diagonal BD inter – InterviewSolution

InterviewSolution

1.

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

Answer»

We have:

∠AFD = ∠EFB (vertically opposite angles)

∵ DA || BC ∴ ∠DAF = ∠BEF (alternative angles)

∆ DAF ~ ∆ BEF (AA similarity theorem)

⇒ AF/EF = FD/FB

Or, AF × FB = FD × EF

This completes the proof.

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