given: x is the midpoint of $overline{vz}$, x is the midpoint of $overline{wy}$
prove: $ riangle vwxcong riangle zyx$
statements reasons

Question

given: x is the midpoint of $overline{vz}$, x is the midpoint of $overline{wy}$
prove: $	riangle vwxcong	riangle zyx$
statements reasons

Accepted Answer

# Explanation:
## Step1: Define mid - point property
Since $X$ is the mid - point of $\overline{VZ}$, then $VX = XZ$ (by the definition of a mid - point, which divides a line segment into two equal parts).
## Step2: Define mid - point property again
Since $X$ is the mid - point of $\overline{WY}$, then $WX=YX$ (by the definition of a mid - point).
## Step3: Identify vertical angles
$\angle VXW=\angle ZXY$ because they are vertical angles (vertical angles are congruent).
## Step4: Apply Side - Angle - Side (SAS) postulate
In $\triangle VWX$ and $\triangle ZYX$, we have $VX = XZ$, $\angle VXW=\angle ZXY$, and $WX = YX$. So, $\triangle VWX\cong\triangle ZYX$ by the SAS congruence postulate.

# Answer:
| Statements | Reasons |
|--|--|
| $X$ is the mid - point of $\overline{VZ}$ | Given |
| $VX = XZ$ | Definition of mid - point |
| $X$ is the mid - point of $\overline{WY}$ | Given |
| $WX = YX$ | Definition of mid - point |
| $\angle VXW=\angle ZXY$ | Vertical angles are congruent |
| $\triangle VWX\cong\triangle ZYX$ | SAS congruence postulate |

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QUESTION IMAGE

Question

Explanation:

Step1: Define mid - point property

Step2: Define mid - point property again

Step3: Identify vertical angles

Step4: Apply Side - Angle - Side (SAS) postulate

Answer:

Statements	Reasons
\(VX = XZ\)	Definition of mid - point
\(X\) is the mid - point of \(\overline{WY}\)	Given
\(WX = YX\)	Definition of mid - point
\(\angle VXW=\angle ZXY\)	Vertical angles are congruent
\(\triangle VWX\cong\triangle ZYX\)	SAS congruence postulate