Question

given: $overline{vu}paralleloverline{qr}$, $overline{vt}paralleloverline{rs}$, $qt = us$. prove: $\triangle qrscong\triangle uvt$. 2. $angle ucongangle q$ 2. given 3. $qt + st = qs$ and $us + st = ut$ 3. betweenness of points 4. $qt = us$ 4. click here to insert 5. $qt + st = us + st$ 5. click here to insert

Explanation:

Step1: Reason for statement 4

The statement "QT = US" is given in the problem - setup, so the reason is "Given".

Step2: Reason for statement 5

Since QT = US (from statement 4), we can substitute US for QT in the equation QT + ST = QS. So the reason for QT + ST = US + ST is the Substitution Property of Equality.

Answer:

1. Given; 5. Substitution Property of Equality