Mathematics
In the given figure, ABCD is a parallelogram, E is a point on BC and the diagonal BD intersects AE at F.
Prove that DF × FE = FB × FA.
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Answer
Since, ABCD is a || gm
∴ AD || BC
In ΔADF and ΔEBF,
∠ADF = ∠EBF [Alternate angles are equal]
∠AFD = ∠EFB [Vertically opposite angles are equal]
∴ ΔADF ∼ ΔEBF (By A.A. axiom)
Corresponding sides of similar triangles are proportional.
DF × FE = FB × FA
Hence, proved that DF × FE = FB × FA.
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