Question

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

statement
1 fg ≅ eh
2 gh ≅ ef
3 eg ≅ eg
4 △efg ≅ △ghe

reason
given
given
reflexive property of congruence
cpctc
definition of congruence
sas

Explanation:

Step1: Identify the congruent sides

We are given that \(\overline{FG}\cong\overline{EH}\), \(\overline{GH}\cong\overline{EF}\), and \(\overline{EG}\cong\overline{EG}\) (by the reflexive property of congruence).

Step2: Apply the SSS (Side - Side - Side) congruence criterion

The SSS congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In \(\triangle EFG\) and \(\triangle GHE\), we have:

• \(FG = EH\) (given)
• \(GH=EF\) (given)
• \(EG = EG\) (reflexive property)

Answer:

SSS (Side - Side - Side)