Question

Given: Angle E ≅ Angle H and G is the midpoint of segment EH.

Answer 1

1. Angle EGF = Angle HGI
Because they are opposite angles (vertical angles)
2. Angle FEG = IHG
Given
3. Triangle EFG is similar to triangle GHI
"angle angle similarity" theorem
4. The two triangles are congruent
"Angle Side Angle" theorem (the segments EG and GH are equal)
5. EF = HI
The corresponding side lengths of two congruent triangles are congruent.