Question

complete the proof that ∠efi ≅ ∠eif.

1. ∠fgh ≅ ∠ghi given
2. (overleftrightarrow{fi}paralleloverleftrightarrow{gh}) given
3. ∠ghi ≅ ∠eif corresponding angles theorem
4. ∠fgh ≅ ∠efi corresponding angles theorem
5. ∠fgh ≅ ∠eif transitive property of congruence
6. ∠efi ≅ ∠eif

Explanation:

Step1: Identify equal - angle relationships

We know from statements 4 ($\angle FGH\cong\angle EFI$) and 5 ($\angle FGH\cong\angle EIF$).

Step2: Apply substitution

Since $\angle FGH$ is congruent to both $\angle EFI$ and $\angle EIF$, we can substitute. If $a = b$ and $a = c$, then $b = c$. In terms of angle - congruence, if $\angle FGH\cong\angle EFI$ and $\angle FGH\cong\angle EIF$, then $\angle EFI\cong\angle EIF$ by the Substitution property.

Answer:

Substitution