Q. 85.0( 1 Vote )

# In the figure, ABCD is a parallelogram. AB is produced to E such that AB = BE. AD produced to F such that AD = DF. Show that ∆FDC ≡ ∆CBE.

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]

A = B [corresponding angles] …(1)

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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