Chapter 3.3, Problem 15PSB

To determine

To prove : The congruency of $\overline{RS}$ with respect to $\overline{VT}$ .

Explanation of Solution

Given information : In this question, we have given that $\angle RST\cong \angle RVT$ and $\angle RVS\cong \angle TSV$

Formula used: Opposite sides and opposite angles of parallelogram are equal.

Proof: As, $\angle RVS\cong \angle TSV$ , which are alternate interior angles,

  $\therefore \overline{RV}\parallel \overline{ST}$

Now, as $\overline{RV}\parallel \overline{ST}$ and $\angle RST\cong \angle RVT$ (opposites angles) ,

Quadrilateral $RSTV$ becomes a parallelogram.

As, opposite sides of parallelogram are equal,

  $\therefore \overline{RS}\cong \overline{VT}$