Question

$$\overleftrightarrow{qs}\parallel\overleftrightarrow{xz}$$ and $$\overleftrightarrow{xz}\parallel\overleftrightarrow{tv}$$. complete the proof that $$\angle qrw\cong\angle puv$$.

Explanation:

Step1: Given information

Given $\overleftrightarrow{QS}\parallel\overleftrightarrow{XZ}$ and $\overleftrightarrow{XZ}\parallel\overleftrightarrow{TV}$

Step2: Corresponding angles

Since $\overleftrightarrow{XZ}\parallel\overleftrightarrow{TV}$ and $PW$ is a transversal, by the Corresponding Angles Theorem, $\angle PUV\cong\angle PYZ$

Step3: Corresponding angles

Since $\overleftrightarrow{QS}\parallel\overleftrightarrow{XZ}$ and $PW$ is a transversal, by the Corresponding Angles Theorem, $\angle PYZ\cong\angle QRW$

Step4: Transitive property

By the Transitive Property of Congruence, if $\angle PUV\cong\angle PYZ$ and $\angle PYZ\cong\angle QRW$, then $\angle QRW\cong\angle PUV$

Answer:

1. Given; 2. Given; 3. Corresponding Angles Theorem; 4. Corresponding Angles Theorem; 5. Transitive Property of Congruence