Question

hj || su and vx || hj. complete the proof that ∠rwx ≅ ∠sty.
statement reason
1 hj || su given
2 vx || hj given
3 ∠rwx ≅ ∠jir corresponding angles theorem
4 ∠jir ≅ ∠sty
5 ∠rwx ≅ ∠sty transitive property of congruence

Explanation:

Step1: Identify given parallel - lines

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

Step2: Find corresponding angles

Since $\overleftrightarrow{VX}\parallel\overleftrightarrow{HJ}$, by the Corresponding Angles Theorem, $\angle RWX\cong\angle JIR$.

Step3: Find another pair of congruent angles

Since $\overleftrightarrow{HJ}\parallel\overleftrightarrow{SU}$, $\angle JIR$ and $\angle STY$ are corresponding angles, so $\angle JIR\cong\angle STY$ (Corresponding Angles Theorem).

Step4: Use transitive property

By the Transitive Property of Congruence, if $\angle RWX\cong\angle JIR$ and $\angle JIR\cong\angle STY$, then $\angle RWX\cong\angle STY$.

Answer:

The reason for $\angle JIR\cong\angle STY$ is the Corresponding Angles Theorem.