Question

given: $overline{vu}paralleloverline{qr}$, $overline{vt}paralleloverline{rs}$, $qt = us$. prove: $\triangle qrscong\triangle uvt$. 1. $overline{vu}paralleloverline{qr}$ 1. given 2. $angle ucongangle q$ 2. click here to insert 3. $qt + st=qs$ and $us + st = ut$ 3. betweenness of points 4. $qt = us$ 4. click here to insert

Explanation:

Step1: Identify angle - congruence reason

When two parallel lines ($\overline{VU}$ and $\overline{QR}$) are cut by a transversal, the alternate - interior angles ($\angle U$ and $\angle Q$) are congruent.

Step2: Identify given statement reason

The statement $QT = US$ is given in the problem statement at the beginning.

Answer:

1. Reason: If two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since $\overline{VU}\parallel\overline{QR}$, $\angle U$ and $\angle Q$ are alternate - interior angles.
2. Reason: Given