Question

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

Explanation:

Step1: Identify corresponding - angles

Since $\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$, $\angle TWX$ and $\angle RTU$ are corresponding angles. So, the reason for $\angle TWX\cong\angle RTU$ is "Corresponding - angles postulate".

Step2: Identify vertical - angles

$\angle RTU$ and $\angle STW$ are vertical angles. Vertical angles are congruent. So, the reason for $\angle RTU\cong\angle STW$ is "Vertical angles are congruent".

Step3: Use transitive property

By the transitive property of congruence, if $\angle TWX\cong\angle RTU$ and $\angle RTU\cong\angle STW$, then $\angle STW\cong\angle TWX$. The reason for $\angle STW\cong\angle TWX$ is "Transitive property of congruence".

Answer:

1. Corresponding - angles postulate
2. Vertical angles are congruent
3. Transitive property of congruence