Question

fg ≅ eh and gh ≅ ef. complete the proof that △efg ≅ △ghe.

1 fg ≅ eh given
2 gh ≅ ef given
3 eg ≅ eg reflexive property of congruence
4 △efg ≅ △ghe

Explanation:

Step1: Recall triangle congruence theorems

We have three pairs of sides: \(\overline{FG}\cong\overline{EH}\), \(\overline{GH}\cong\overline{EF}\), and \(\overline{EG}\cong\overline{EG}\).

Step2: Apply SSS theorem

The SSS (Side - Side - Side) congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Here, in \(\triangle EFG\) and \(\triangle GHE\), we have \(FG = EH\), \(GH=EF\), and \(EG = EG\) (common side).

Answer:

SSS