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

Answer:
Step-by-step explanation:
Step # Statement Reason
2 ∠BCA ≅ ∠DAC Alternate interior angles
3 FA = AE + EF Segment addition postulate
4 CE = CF + EF Segment addition postulate
5 FA ≅ CE Transitive property of equality
6 △GEC ≅ △HFA ASA postulate (two angles and the
included side congruence)
<GEC=<HFA
As
Also
Henceforth
△GEC ≅ △HFA(ASA)