1. **State the problem:** We need to prove that the line segment $\overline{HI}$ is congruent to the line segment $\overline{XW}$ by using the given triangles $WVX$ and $HJI$ and their corresponding parts. 2. **Identify corresponding parts:** From the problem, the triangles $WVX$ and $HJI$ have the following correspondences: - $W$ corresponds to $H$ - $V$ corresponds to $J$ - $X$ corresponds to $I$ 3. **Given information:** - $\overline{WV} \cong \overline{HJ}$ (marked equal segments) - $\overline{VX} \cong \overline{JI}$ (marked equal segments) - $\angle W \cong \angle H$ and $\angle X \cong \angle I$ (marked equal angles) 4. **Use the Triangle Congruence Postulate:** Since two sides and the included angle of triangle $WVX$ are congruent to two sides and the included angle of triangle $HJI$, by the SAS (Side-Angle-Side) Postulate, we conclude: $$\triangle WVX \cong \triangle HJI$$ 5. **Corresponding parts of congruent triangles are congruent (CPCTC):** Since the triangles are congruent, all corresponding parts are congruent. Therefore, $$\overline{HI} \cong \overline{XW}$$ **Final answer:** $\overline{HI} \cong \overline{XW}$ by CPCTC after proving $\triangle WVX \cong \triangle HJI$ using SAS.