Answer :

Given: Parallelogram ABCD and AB = BE and AD = FD

To prove: Δ FDC ≡ ΔCBE

Construction: Join DB

Proof:

We know that,

AB = DC [ opposite sides of parallelogram]

BE = DC [AB = BE, because B is the midpoint of AE]

Similarly,

AD = BC [ opposite sides of parallelogram]

DF = BC [ AD = DF, because B is the midpoint of AE]

Now, AD||BC and AB

∠ A = ∠ B [corresponding angles] …(1)

Now, AB||CD and AD

∠ A = ∠ D [corresponding angles] …(2)

∴ ∠ B = ∠ D (From 1 and 2)

In Δ FDC and Δ CBE

FD = CB [Proved Above]

DC = BE [Proved Above]

∠ D = ∠ B [Proved Above]

Thus, Δ FDC ≡ Δ CBE

Hence Proved.

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