Question

$$\overline { vy } \perp \overline { wx }$$ and $$\angle xvy \cong \angle w v y$$. complete the proof that $$\overline { xy } \cong \overline { wy }$$.

statement	reason
2 $$\angle xvy \cong \angle w v y$$	given
3 $$\angle v y w \cong \angle v y x$$	all right angles are congruent
4 $$\overline { vy } \cong \overline { vy }$$	reflexive property of congruence
5

Explanation:

Step1: Identify congruent triangles

From steps 2, 3, 4: $\angle XVY \cong \angle WVY$, $\angle VYW \cong \angle VYX$, $\overline{VY} \cong \overline{VY}$. So $\triangle VYW \cong \triangle VYX$ by ASA.

Step2: Corresponding sides are congruent

Corresponding sides of congruent triangles are congruent: $\overline{XY} \cong \overline{WY}$.

Answer:

$\overline{XY} \cong \overline{WY}$ (by ASA congruence of $\triangle VYW$ and $\triangle VYX$, then CPCTC)