Question

Given: ABCDis a parallelogram ∠GEC ≅ ∠HFA and AE ≅FC.
Prove △GEC ≅ △HFA.

Answer 1

<GEC=<HFA

As

• AE=FC
• FE=FE(Common in both

So

• FE+AE=FE+CE

Cancel FE

• A F=E C

Also

<CAH=<GCE(Alternative interior angles)

Henceforth

△GEC ≅ △HFA(ASA)