Question

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

Answer 1

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Answer 2

Answer:

Given: ABCD is a parallelogram and E is a point on BC. The diagonal BD intersects AE at F.

To prove :- AF x FB = EF x FD.

Proof:- Since ABCD is a paralellogram, then its opposite sides must be parallel.

∴ In Δ ADF and Δ EBF

∠FDA=∠EBF and ∠FAD=∠FEB  [Alternate interior angles]

∠AFD=∠BFE [vertically opposite angles]

∴ By AAA similarity rule

Δ ADF ≈ Δ EBF

Also, the correspondingsides of similar triangles are proportional.

∴$\frac{AF}{FD}=\frac{EF}{FB}\\\Rightarrow\ AF\times FB=EF\times FD$

Hence proved.