Question

complete the proof that ∠utw ≅ ∠twv.
statement reason
1 vx || su given
2 ∠twv ≅ ∠rts
3 ∠rts ≅ ∠utw
4 ∠utw ≅ ∠twv transitive property of congruence

Explanation:

Step1: Identify corresponding - angles

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