Question

complete the proof that ∠yxz≅∠sut. statement 1. wy || pr 2. tv || pr 3. ∠yxz≅∠rqz 4. ∠rqz≅∠sut 5. ∠yxz≅∠sut reason given given

Explanation:

Step1: Identify vertical - angle property

Vertical angles are congruent. Since $\angle YXZ$ and $\angle RQZ$ are vertical angles, $\angle YXZ\cong\angle RQZ$ (Vertical - Angles Theorem).

Step2: Identify corresponding - angle property

Given $\overleftrightarrow{TV}\parallel\overleftrightarrow{PR}$, $\angle RQZ$ and $\angle SUT$ are corresponding angles. By the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, corresponding angles are congruent. So $\angle RQZ\cong\angle SUT$.

Step3: Use the transitive property of congruence

Since $\angle YXZ\cong\angle RQZ$ and $\angle RQZ\cong\angle SUT$, by the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$ for congruent angles), $\angle YXZ\cong\angle SUT$.

Answer:

1. Vertical - Angles Theorem; 4. Corresponding Angles Postulate; 5. Transitive Property of Congruence