Question

$\angle rts \cong \angle xwy$. complete the proof that $\overleftrightarrow{su} \parallel \overleftrightarrow{vx}$.
(image of lines and angles with a table for proof statements and reasons:

1. $\angle rts \cong \angle xwy$ (reason blank)
2. $\angle rts \cong \angle utw$ (reason blank)
3. $\angle xwy \cong \angle utw$ (reason blank)
4. $\overleftrightarrow{su} \parallel \overleftrightarrow{vx}$ (reason blank))

Explanation:

Step1: Given

\(\angle RTS\cong\angle XWY\) (Given)

Step2: Vertical angles are congruent

\(\angle RTS\cong\angle UTW\) (Vertical angles are congruent)

Step3: Transitive property of congruence

Since \(\angle RTS\cong\angle XWY\) and \(\angle RTS\cong\angle UTW\), then \(\angle XWY\cong\angle UTW\) (Transitive property of congruence: if \(a = b\) and \(a = c\), then \(b = c\))

Step4: Corresponding angles converse

If \(\angle XWY\cong\angle UTW\), then \(\overleftrightarrow{SU}\parallel\overleftrightarrow{VX}\) (Corresponding angles converse: if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel)

Answer:

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