Question

17. ABCD is a parallelogram. The sides AB, AD
are produced to E, F so that AB = BE and AD =
DF. Prove that the triangles BEC and DCF are
congruent.
.... please answer ASAP ....​

Answer 1

Given:

AB = BE = CD  and  BC = AD = DF

in a Parallelogram ∠BAD = ∠CDF

in Parallel Lines (Congugate Angles) ∠EBC = ∠BAD

So, ∠BAD = ∠CDF = ∠EBC

To Prove :

ΔBEC ≅ ΔDCF

Proof :

Side -> EB = CD

Angle -> ∠CDF = ∠EBC

Side -> BC = DF

Hence, Through SAS ΔBEC ≅ ΔDCF