Question

∠prs ≅ ∠tuw. complete the proof that (overleftrightarrow{tv}paralleloverleftrightarrow{qs}).
statement reason
1 ∠prs ≅ ∠tuw
2 ∠prs ≅ ∠qru
3 ∠tuw ≅ ∠qru
4 (overleftrightarrow{tv}paralleloverleftrightarrow{qs})

Explanation:

Step1: Given information

Given that $\angle PRS\cong\angle TUW$

Step2: Vertical - angle property

$\angle PRS$ and $\angle QRU$ are vertical angles, so $\angle PRS\cong\angle QRU$ (Vertical angles are congruent)

Step3: Transitive property of congruence

Since $\angle PRS\cong\angle TUW$ and $\angle PRS\cong\angle QRU$, then $\angle TUW\cong\angle QRU$ (If $a = b$ and $a = c$, then $b = c$)

Step4: Corresponding - angles postulate

$\angle TUW$ and $\angle QRU$ are corresponding angles. If corresponding angles are congruent, then the lines are parallel. So, $\overleftrightarrow{TV}\parallel\overleftrightarrow{QS}$ (Corresponding angles postulate: If two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel)

Answer:

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