Question

statement reason 1 rt || hj given 2 hj || uw given 3 ∠wvx ≅ ∠jix corresponding angles theorem 4 ∠jix ≅ ∠qsr i 5 ∠qsr ≅ ∠wvx transitive property of congruence

Explanation:

Step1: Recall parallel - line properties

Since $\overleftrightarrow{RT}\parallel\overleftrightarrow{HJ}$ and $\overleftrightarrow{HJ}\parallel\overleftrightarrow{UW}$, we use the fact that if two lines are parallel to the same line, then they are parallel to each other. Also, when two parallel lines are cut by a transversal, corresponding angles are congruent.

Step2: Identify corresponding - angle relationship for $\angle JIX$ and $\angle QSR$

$\angle JIX$ and $\angle QSR$ are corresponding angles formed by the parallel lines $\overleftrightarrow{RT}$ and $\overleftrightarrow{HJ}$ cut by the transversal $\overleftrightarrow{QS}$. According to the Corresponding Angles Theorem, if two parallel lines are cut by a transversal, then the corresponding angles are congruent. So the reason for $\angle JIX\cong\angle QSR$ is the Corresponding Angles Theorem.

Answer:

Corresponding Angles Theorem