Question

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complete the proof that ∠stw≅∠twx.
statement reason

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

properties of addition, subtraction, multiplication, and division
reflexive property of congruence
reflexive property of equality
substitution
transitive property of congruence
transitive property of equality

Explanation:

Step1: Recall the given statements

We are given $\overrightarrow{VX}\parallel\overrightarrow{SU}$, and by corresponding - angles theorem $\angle TWX\cong\angle RTU$, and by vertical - angle theorem $\angle RTU\cong\angle STW$.

Step2: Use the transitive property of congruence

The transitive property of congruence states that if $\angle A\cong\angle B$ and $\angle B\cong\angle C$, then $\angle A\cong\angle C$. Here, since $\angle TWX\cong\angle RTU$ and $\angle RTU\cong\angle STW$, we can substitute $\angle RTU$ to get $\angle STW\cong\angle TWX$.

Answer:

Transitive Property of Congruence