y is the midpoint of $\overline{wx}$. complete the proof that $\triangle vxy \cong \triangle vwy$.

| statement | reason |
| --- | --- |
| 1. y is the midpoint of $\overline{wx}$ | given |
| 2. $\overline{vy} \perp \overline{wx}$ | given |
| 3. $\angle vyw \cong \angle vyx$ | all right angles are congruent |
| 4. $\overline{wy} \cong \overline{xy}$ | definition of midpoint |
| 5. | reflexive property of congruence |

Question

y is the midpoint of $\overline{wx}$. complete the proof that $\triangle vxy \cong \triangle vwy$.

| statement | reason |
| --- | --- |
| 1. y is the midpoint of $\overline{wx}$ | given |
| 2. $\overline{vy} \perp \overline{wx}$ | given |
| 3. $\angle vyw \cong \angle vyx$ | all right angles are congruent |
| 4. $\overline{wy} \cong \overline{xy}$ | definition of midpoint |
| 5.  | reflexive property of congruence |

Accepted Answer

# Explanation:
## Step1: Recall Reflexive Property
The Reflexive Property of Congruence states that a segment or angle is congruent to itself. For triangles $ \triangle VXY $ and $ \triangle VWY $, the common side is $ \overline{VY} $. So we need to identify that $ \overline{VY} \cong \overline{VY} $ (or $ VY = VY $) as the statement for the Reflexive Property.
## Step2: Formulate the Statement
Since the reason is the Reflexive Property of Congruence, the statement should be that $ \overline{VY} $ is congruent to itself, i.e., $ \overline{VY} \cong \overline{VY} $ (or $ VY = VY $).

# Answer:
$ \overline{VY} \cong \overline{VY} $ (or $ VY = VY $)

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QUESTION IMAGE

Question

Explanation:

Step1: Recall Reflexive Property

Step2: Formulate the Statement

Answer:

statement	reason
2. \\(\overline{vy} \perp \overline{wx}\\)	given
3. \\(\angle vyw \cong \angle vyx\\)	all right angles are congruent
4. \\(\overline{wy} \cong \overline{xy}\\)	definition of midpoint
5.	reflexive property of congruence