ABCD is a parallelogram The sides AB and AD are produced to E and F respectively, such that AB=BE and AD=DF.Then prove ?BEC??DCF.

Answer:

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Corresponding angles for parallel lines AB and CD

∠BAD = ∠CDF

Corresponding angles for parallel lines AB and CD

∠BAD = ∠CBE

Thus, ∠CDF = ∠CBE……………………….(1)

ABCD is a parallelogram so we know that

AD = BC

Given

AD = DF

∴ DF=BC…………………….. (2)

Similarly,

BE = CD…………………………(3)

Now, consider ?CDF and ?CBE

From equation (1)

∠CDF = ∠CBE

From equation (2)

FD = BC

From equation (3)

BE = CD

Thus from SAS rule

?FDC ≅ ?CBE

?BEC ≅ ?DCF

Hence the prove.

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