Question

complete the proof that wy || tv. 1. statement: ∠suv ≅ ∠wxz, reason: given. 2. statement: ∠suv ≅ ∠tux, reason: vertical angle theorem. 3. statement: ∠wxz ≅ ∠tux, reason: angles forming a linear - pair sum to 180°. 4. statement: wy || tv, reason: corresponding angles theorem. definition of supplementary angles

Explanation:

Step1: Given information

We are given that $\angle SUV\cong\angle WXZ$. This is the starting - point of our proof.

Step2: Use vertical - angle property

$\angle SUV\cong\angle TUX$ because vertical angles are congruent. (Vertical Angle Theorem)

Step3: Transitive property of congruence

Since $\angle SUV\cong\angle WXZ$ and $\angle SUV\cong\angle TUX$, by the transitive property of congruence, we have $\angle WXZ\cong\angle TUX$.

Step4: Conclude parallel lines

$\overrightarrow{WY}\parallel\overrightarrow{TV}$ because corresponding angles ($\angle WXZ$ and $\angle TUX$) are congruent. (Corresponding Angles Theorem)

Answer:

1. $\angle SUV\cong\angle WXZ$ - Given
2. $\angle SUV\cong\angle TUX$ - Vertical Angle Theorem
3. $\angle WXZ\cong\angle TUX$ - Transitive property of congruence
4. $\overrightarrow{WY}\parallel\overrightarrow{TV}$ - Corresponding Angles Theorem