Question

complete the proof that ∠rtu≅∠vwy.
statement reason

1. $overleftrightarrow{vx}paralleloverleftrightarrow{su}$ given
2. ∠vwy≅∠stw corresponding angles theorem
3. ∠stw≅∠rtu vertical angle theorem
4. ∠rtu≅∠vwy

Explanation:

Step1: Given parallel lines

We are given that $\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$.

Step2: Use corresponding - angles theorem

Since $\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$, by the Corresponding Angles Theorem, $\angle VWY\cong\angle STW$.

Step3: Use vertical - angles theorem

$\angle STW$ and $\angle RTU$ are vertical angles. By the Vertical Angle Theorem, $\angle STW\cong\angle RTU$.

Step4: Apply transitive property of congruence

If $\angle VWY\cong\angle STW$ and $\angle STW\cong\angle RTU$, then by the transitive property of congruence, $\angle RTU\cong\angle VWY$.

Answer:

Transitive property of congruence