z is the midpoint of $\overline{wy}$ and $\overline{vx}$. complete the proof that $\triangle vyz \cong \triangle xwz$.

| statement | reason |
| --- | --- |
| 1 $z$ is the midpoint of $\overline{wy}$ | given |
| 2 $z$ is the midpoint of $\overline{vx}$ | given |
| 3 $\overline{wz} \cong \overline{yz}$ | definition of midpoint |
| 4 $\overline{vz} \cong \overline{xz}$ | definition of midpoint |
| 5 $\angle vzy \cong \angle wzx$ | vertical angle theorem |
| 6 $\triangle vyz \cong \triangle xwz$ | |

Question

z is the midpoint of $\overline{wy}$ and $\overline{vx}$. complete the proof that $\triangle vyz \cong \triangle xwz$.

| statement | reason |
| --- | --- |
| 1 $z$ is the midpoint of $\overline{wy}$ | given |
| 2 $z$ is the midpoint of $\overline{vx}$ | given |
| 3 $\overline{wz} \cong \overline{yz}$ | definition of midpoint |
| 4 $\overline{vz} \cong \overline{xz}$ | definition of midpoint |
| 5 $\angle vzy \cong \angle wzx$ | vertical angle theorem |
| 6 $\triangle vyz \cong \triangle xwz$ |  |

Accepted Answer

# Explanation:
## Step1: Match statement to midpoint rule
Statement 3: $\overline{WZ} \cong \overline{YZ}$
Reason: Definition of midpoint (since Z is midpoint of $\overline{WY}$)
## Step2: Match statement to midpoint rule
Statement 4: $\overline{VZ} \cong \overline{XZ}$
Reason: Definition of midpoint (since Z is midpoint of $\overline{VX}$)
## Step3: Match statement to vertical angle rule
Statement 5: $\angle VZY \cong \angle WZX$
Reason: Vertical Angle Theorem
## Step4: Prove triangle congruence
Statement 6: $	riangle VYZ \cong 	riangle XWZ$
Reason: Side-Angle-Side (SAS) Congruence Postulate
# Answer:
| Statement | Reason |
|-----------|--------|
| 1. $Z$ is the midpoint of $\overline{WY}$ | Given |
| 2. $Z$ is the midpoint of $\overline{VX}$ | Given |
| 3. $\overline{WZ} \cong \overline{YZ}$ | Definition of midpoint |
| 4. $\overline{VZ} \cong \overline{XZ}$ | Definition of midpoint |
| 5. $\angle VZY \cong \angle WZX$ | Vertical Angle Theorem |
| 6. $	riangle VYZ \cong 	riangle XWZ$ | Side-Angle-Side (SAS) Congruence Postulate |

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Match statement to midpoint rule

Step2: Match statement to midpoint rule

Step3: Match statement to vertical angle rule

Step4: Prove triangle congruence

Answer:

statement	reason
2 \\(z\\) is the midpoint of \\(\overline{vx}\\)	given
3 \\(\overline{wz} \cong \overline{yz}\\)	definition of midpoint
4 \\(\overline{vz} \cong \overline{xz}\\)	definition of midpoint
5 \\(\angle vzy \cong \angle wzx\\)	vertical angle theorem
6 \\(\triangle vyz \cong \triangle xwz\\)

Statement	Reason
2. $Z$ is the midpoint of $\overline{VX}$	Given
3. $\overline{WZ} \cong \overline{YZ}$	Definition of midpoint
4. $\overline{VZ} \cong \overline{XZ}$	Definition of midpoint
5. $\angle VZY \cong \angle WZX$	Vertical Angle Theorem
6. $\triangle VYZ \cong \triangle XWZ$	Side-Angle-Side (SAS) Congruence Postulate