Question

$\overline{ei}\perp\overline{eg},\angle gfh\cong\angle efi,\overline{ei}\cong\overline{gh}$, and $\overline{eg}\perp\overline{gh}$. complete the proof that $\triangle efi\cong\triangle gfh$.

Explanation:

1. The first statement is given directly in the problem.
2. The second statement about congruent angles is also provided as a given.
3. The third statement regarding congruent segments is a given condition.
4. The fourth statement about perpendicular segments is a given.
5. Since both $\angle E$ and $\angle G$ are right angles (from perpendicular sides), all right angles are congruent.
6. Using the ASA congruence criterion: $\angle E \cong \angle G$, $\overline{EI} \cong \overline{GH}$, and $\angle EFI \cong \angle GFH$.

Answer:

1. Given
2. Given
3. Given
4. Given
5. All right angles are congruent
6. ASA Congruence Criterion