given : $\overline{vw} \parallel \overline{zm}$$\frac{vw}{zm} = \frac{wm}{my}$prove : $\angle v \cong \angle z$$\begin{array}{|c|c|}\hline\text{statement}&\text{reason}\\\hline\overline{vw} \parallel \overline{zm}&\\\hline\angle vwm \cong \angle zmy&\\\hline\frac{vw}{zm} = \frac{wm}{my}&\\\hline\triangle vwm \sim \triangle zmy&\\\hline\angle v \cong \angle z&\\\hline\end{array}$corresponding angles of similar triangles are congruent \ \ sas similaritygiven \ \ corresponding angles \ \ given

Question

given : $\overline{vw} \parallel \overline{zm}$$\frac{vw}{zm} = \frac{wm}{my}$prove : $\angle v \cong \angle z$$\begin{array}{|c|c|}\hline\text{statement}&\text{reason}\\\hline\overline{vw} \parallel \overline{zm}&\\\hline\angle vwm \cong \angle zmy&\\\hline\frac{vw}{zm} = \frac{wm}{my}&\\\hline\triangle vwm \sim \triangle zmy&\\\hline\angle v \cong \angle z&\\\hline\end{array}$corresponding angles of similar triangles are congruent  \ \ sas similaritygiven  \ \ corresponding angles  \ \ given

Accepted Answer

# Explanation:
## Step1: Justify $\overline{VW} \parallel \overline{ZM}$
The statement $\overline{VW} \parallel \overline{ZM}$ is given, so the reason is "Given".

## Step2: Justify $\angle VWM \cong \angle ZMY$
Since $\overline{VW} \parallel \overline{ZM}$ and $WY$ is a transversal, $\angle VWM$ and $\angle ZMY$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are congruent, so the reason is "Corresponding Angles".

## Step3: Justify $\frac{VW}{ZM} = \frac{WM}{MY}$
The proportion $\frac{VW}{ZM} = \frac{WM}{MY}$ is given, so the reason is "Given".

## Step4: Justify $\triangle VWM \sim \triangle ZMY$
We have $\angle VWM \cong \angle ZMY$ (from Step 2) and $\frac{VW}{ZM} = \frac{WM}{MY}$ (from Step 3). By the SAS (Side - Angle - Side) Similarity criterion, if two sides of one triangle are in proportion to two sides of another triangle and the included angles are congruent, then the triangles are similar. So the reason is "SAS Similarity".

## Step5: Justify $\angle V \cong \angle Z$
Since $\triangle VWM \sim \triangle ZMY$, corresponding angles of similar triangles are congruent. So $\angle V$ and $\angle Z$ are corresponding angles of similar triangles, so the reason is "Corresponding Angles of Similar Triangles are Congruent".

# Answer:
| Statement | Reason |
| --- | --- |
| $\overline{VW} \parallel \overline{ZM}$ | Given |
| $\angle VWM \cong \angle ZMY$ | Corresponding Angles |
| $\frac{VW}{ZM} = \frac{WM}{MY}$ | Given |
| $\triangle VWM \sim \triangle ZMY$ | SAS Similarity |
| $\angle V \cong \angle Z$ | Corresponding Angles of Similar Triangles are Congruent |

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QUESTION IMAGE

Question

Explanation:

Step1: Justify \(\overline{VW} \parallel \overline{ZM}\)

Step2: Justify \(\angle VWM \cong \angle ZMY\)

Step3: Justify \(\frac{VW}{ZM} = \frac{WM}{MY}\)

Step4: Justify \(\triangle VWM \sim \triangle ZMY\)

Step5: Justify \(\angle V \cong \angle Z\)

Answer:

Statement	Reason
\(\angle VWM \cong \angle ZMY\)	Corresponding Angles
\(\frac{VW}{ZM} = \frac{WM}{MY}\)	Given
\(\triangle VWM \sim \triangle ZMY\)	SAS Similarity
\(\angle V \cong \angle Z\)	Corresponding Angles of Similar Triangles are Congruent