Question

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

Explanation:

Step1: Justify $\angle U\cong\angle Q$

If two parallel lines are cut by a transversal, corresponding - angles are congruent. Here, $\overline{VU}\parallel\overline{QR}$ and they are cut by a transversal (not explicitly named in the diagram but implied), so $\angle U\cong\angle Q$.

Step2: Justify $QT = US$

It is given in the problem statement that $QT = US$.

Answer:

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