Question

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

Answer 1

<GEC=<HFA

As

• AE=FC
• A F=E C

Also

• <BCA=<CAH(Alternative interior)

Henceforth

△GEC ≅ △HFA(ASA)

Answer 2

• See below

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)