Question

ABCD is parallelogram, it's diagonals intersect at M, E belong to DM where DE=2EM , CE cut AD at F.
Prove that: AF=FD

Answer 1

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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

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Solution

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In △DFA and △EFB

∠DFA=∠EFB (Vertically Opposite Angle)

∠ADB=∠FBE (AD || BC)

∠DAF=∠FEB (AD || BC)

According to AAA congruency rule

△DFA∼△EFB

Hence,

FE

AF

=

FB

DF

⇒AF×FB=EF×FD

so