Question

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

	statement	reason
1	△efh is equilateral	given
2	\\(\overline{fg} \cong \overline{ei}\\)	given
3	\\(\angle hei \cong \angle gfh\\)	given
4

Explanation:

Step1: Identify equal sides from equilateral $\triangle EFH$

Since $\triangle EFH$ is equilateral, all sides are congruent: $\overline{FH} \cong \overline{EH}$

Step2: List all congruent parts

We have:

1. $\overline{FG} \cong \overline{EI}$ (Given)
2. $\angle GFH \cong \angle HEI$ (Given)
3. $\overline{FH} \cong \overline{EH}$ (From Step1)

Step3: Apply SAS congruence

Two sides and the included angle of $\triangle FGH$ are congruent to two sides and the included angle of $\triangle EIH$, so by the Side-Angle-Side (SAS) Congruence Postulate, $\triangle FGH \cong \triangle EIH$

Answer:

Statement 4: $\overline{FH} \cong \overline{EH}$

Reason 4: Sides of equilateral triangle are congruent

Statement 5: $\triangle FGH \cong \triangle EIH$

Reason 5: SAS Congruence Postulate