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

Given ABCDis A Parallelogram GEC HFA And AE FC Prove GEC HFA class=

Sagot :

Mhanifaidn

Answer:

  • See below

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

  • AE=FC
  • A F=E C

Also

  • <BCA=<CAH(Alternative interior)

Henceforth

△GEC ≅ △HFA(ASA)

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