Question

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 1

QUESTION :-

=> 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.

SOLUTION :-

=>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.

Answer 2

Answer:

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