Question

δefh is equilateral. complete the proof that δfhi ≅ δhig.
1 δefh is equilateral
2 ∠gfh ≅ ∠hei
3 overline{ei} ≅ overline{fg}
4 overline{eh} ≅ overline{fh}
5 δehi ≅ δfhg

Explanation:

Step1: Given

The problem states that $\triangle EFH$ is equilateral. So, the reason for statement 1 is "Given".

Step2: Given

The problem provides that $\angle GFH\cong\angle HEI$. So, the reason for statement 2 is "Given".

Step3: Given

The problem provides that $\overline{EI}\cong\overline{FG}$. So, the reason for statement 3 is "Given".

Step4: Definition of equilateral triangle

Since $\triangle EFH$ is equilateral, all its sides are equal. So, $\overline{EH}\cong\overline{FH}$ by the definition of an equilateral triangle.

Step5: SAS (Side - Angle - Side) Congruence Criterion

We have $\overline{EI}\cong\overline{FG}$ (side), $\angle GFH\cong\angle HEI$ (angle), and $\overline{EH}\cong\overline{FH}$ (side). So, $\triangle EHI\cong\triangle FHG$ by the SAS congruence criterion.

Answer:

1. Given
2. Given
3. Given
4. Definition of equilateral triangle
5. SAS (Side - Angle - Side) Congruence Criterion