Question

complete the proof that ∠tw v≅∠utw.
statement reason

1. (overrightarrow{su}paralleloverrightarrow{vx}) given
2. ∠tw v≅∠rts
3. ∠rts≅∠utw
4. ∠tw v≅∠utw transitive property of congruence

Explanation:

Step1: Identify corresponding - angles

Since $\overrightarrow{SU}\parallel\overrightarrow{VX}$, $\angle TW V$ and $\angle RTS$ are corresponding angles. By the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then the corresponding angles are congruent. So the reason for $\angle TW V\cong\angle RTS$ is "Corresponding Angles Postulate".

Step2: Identify vertical - angles

$\angle RTS$ and $\angle UTW$ are vertical angles. By the Vertical Angles Theorem, vertical angles are congruent. So the reason for $\angle RTS\cong\angle UTW$ is "Vertical Angles Theorem".

Answer:

1. Corresponding Angles Postulate
2. Vertical Angles Theorem