Question

complete the proof that vx || su.
statement reason
1 ∠xwy ≅ ∠rts given
2 ∠rts ≅ ∠utw vertical angle theorem
3 ∠xwy ≅ ∠utw transitive property of congruence
4 vx || su con

Explanation:

Step1: Given angle equality

We are given that $\angle XWY\cong\angle RTS$.

Step2: Use vertical - angle theorem

By the Vertical Angle Theorem, $\angle RTS\cong\angle UTW$ since they are vertical angles.

Step3: Apply transitive property

Using the Transitive Property of Congruence, since $\angle XWY\cong\angle RTS$ and $\angle RTS\cong\angle UTW$, we have $\angle XWY\cong\angle UTW$.

Step4: Use converse of corresponding - angles theorem

$\angle XWY$ and $\angle UTW$ are corresponding angles. By the Converse of the Corresponding Angles Theorem, if corresponding angles are congruent, then the lines are parallel. So, $\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$.

Answer:

The reason for statement 4 is "Converse of Corresponding Angles Theorem".