Question

complete the proof that ∠yxz≅∠sut.
statement reason
1 (overleftrightarrow{ik}paralleloverleftrightarrow{wy}) given
2 (overleftrightarrow{ik}paralleloverleftrightarrow{tv}) given
3 ∠sut≅∠ijs corresponding angles theorem
4 ∠ijs≅∠yxz alternate exterior angles theorem
5 ∠yxz≅∠sut

Explanation:

Step1: Recall transitive property of congruence

If $\angle A\cong\angle B$ and $\angle B\cong\angle C$, then $\angle A\cong\angle C$.

Step2: Identify relevant congruent - angle pairs

We have $\angle SUT\cong\angle IJS$ (from step 3) and $\angle IJS\cong\angle YXZ$ (from step 4).

Step3: Apply transitive property

Since $\angle SUT\cong\angle IJS$ and $\angle IJS\cong\angle YXZ$, by the transitive property of congruence, $\angle YXZ\cong\angle SUT$.

Answer:

Transitive property of congruence