Question

gi || tv and gi || qs. complete the proof that m∠srw + m∠ruv = 180.

Explanation:

Step1: Identify parallel lines

Given $\overleftrightarrow{GI}\parallel\overleftrightarrow{TV}$ and $\overleftrightarrow{GI}\parallel\overleftrightarrow{QS}$. Since $\overleftrightarrow{TV}\parallel\overleftrightarrow{QS}$ (lines parallel to the same line are parallel to each other).

Step2: Use same - side interior angles property

$\angle SRW$ and $\angle RUV$ are same - side interior angles for the parallel lines $\overleftrightarrow{TV}$ and $\overleftrightarrow{QS}$ with transversal $\overleftrightarrow{PU}$. By the same - side interior angles postulate, if two parallel lines are cut by a transversal, then the same - side interior angles are supplementary. So $m\angle SRW + m\angle RUV=180^{\circ}$.

Answer:

The proof is completed by first using the transitive property of parallel lines to show $\overleftrightarrow{TV}\parallel\overleftrightarrow{QS}$ and then applying the same - side interior angles postulate.