Question

ABCD is a parallelogram. The sides AB and AD are produced such that AB = BE and AD = DF.

Prove that, △BEC ≅△DCF​

Answer 1

Step-by-step explanation:

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.