Question

complete the proof that ( overleftrightarrow{uw} parallel overleftrightarrow{rt} ).

Explanation:

Step1: Recall the converse of corresponding angles theorem

The converse of corresponding angles theorem states that if two lines are cut by a transversal such that a pair of corresponding angles are congruent, then the two lines are parallel.

Step2: Analyze the given congruent angles

We have shown that \( \angle QSR\cong\angle QVU\). Here, \( \angle QSR\) and \( \angle QVU\) are corresponding angles formed by the transversal \( XQ\) intersecting the lines \( RT\) and \( UW\).

Answer:

Converse of Corresponding Angles Theorem