Question

statement reason 1. $overleftrightarrow{su}paralleloverleftrightarrow{fv}$ given 2. $overleftrightarrow{fv}paralleloverleftrightarrow{vx}$ given 3. $angle{rwv}congangle{fgr}$ corresponding angles theorem 4. $angle{fgr}congangle{uty}$ 5. $angle{uty}congangle{rwv}$ alternate exterior angles theorem alternate interior angles theorem converse of alternate exterior angles theorem converse of alternate interior angles theorem converse of corresponding angles theorem converse of same - side interior angles theorem

Explanation:

Step1: Identify parallel - line relationships

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

Step2: Analyze angle - congruence statements

We know $\angle RW V\cong\angle FGR$ by the Corresponding Angles Theorem.

Step3: Find the reason for $\angle FGR\cong\angle UTY$

Since $\overleftrightarrow{FV}\parallel\overleftrightarrow{VX}$, and $\angle FGR$ and $\angle UTY$ are corresponding angles formed by a transversal intersecting these parallel lines, the reason is the Corresponding Angles Theorem.

Answer:

Corresponding Angles Theorem