Question

△efh is equilateral. complete the proof that △fgh ≅ △eih.

statement
1 △efh is equilateral
2 overline{fg} ≅ overline{ei}
3 ∠gfh ≅ ∠hei
4 overline{eh} ≅ overline{fh}
5 △fgh ≅ △eih

reason
given
given
given
definition of equilateral triangle

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

Step2: Identify the corresponding parts in \(\triangle FGH\) and \(\triangle EIH\)

We have \(\overline{FG}\cong\overline{EI}\) (given), \(\angle GFH\cong\angle HEI\) (given), and \(\overline{FH}\cong\overline{EH}\) (from the definition of an equilateral triangle \(\triangle EFH\)).

Answer:

SAS (Side - Angle - Side) congruence criterion.