Question

∠suv≅∠wxz. complete the proof that (overleftrightarrow{wy}paralleloverleftrightarrow{tv}).
statement reason
1 ∠suv≅∠wxz given
2 ∠suv≅∠tux
3 ∠wxz≅∠tux
4 (overleftrightarrow{wy}paralleloverleftrightarrow{tv})

Explanation:

Step1: Identify vertical - angle relationship

$\angle SUV$ and $\angle TUX$ are vertical angles. Vertical angles are congruent. So, $\angle SUV\cong\angle TUX$ because vertical angles are congruent.

Step2: Use transitive property

Since $\angle SUV\cong\angle WXZ$ (given) and $\angle SUV\cong\angle TUX$, by the transitive property of congruence, $\angle WXZ\cong\angle TUX$.

Step3: Apply corresponding - angles postulate

$\angle WXZ$ and $\angle TUX$ are corresponding angles. If corresponding angles are congruent, then the lines are parallel. So, $\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}$ by the corresponding - angles postulate.

Answer:

1. Reason: Vertical angles are congruent.
2. Reason: Transitive property of congruence.
3. Reason: Corresponding - angles postulate.