Question

complete the proof that ∠stw≅∠twx.
statement reason
1 vx || su given
2 ∠twx≅∠rtu
3 ∠rtu≅∠stw
4 ∠stw≅∠twx transitive property of congruence

Explanation:

Step1: Identify corresponding - angles

Since $\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$, $\angle TWX$ and $\angle RTU$ 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 statement 2 is "Corresponding Angles Postulate".

Step2: Identify vertical - angles

$\angle RTU$ and $\angle STW$ are vertical angles. By the Vertical Angles Theorem, vertical angles are congruent. So the reason for statement 3 is "Vertical Angles Theorem".

Answer:

1. Corresponding Angles Postulate
2. Vertical Angles Theorem