Chapter 4.3, Problem 5ST1

To determine

Whether the given two triangles congruent.

Answer to Problem 5ST1

  $\Delta TPR\cong \Delta TSR$

Explanation of Solution

Given information :

Giventwo triangles

  

From the $\Delta PTR,$

  $\angle PRT=180-\left(50+60\right)$

  $\begin{array}{l}=180-110\\ \therefore \angle PRT=70\end{array}$

Similar way, in $\Delta RTS,$

  $\angle RTS=180-\left(70+60\right)$

  $\begin{array}{l}=180-130\\ \therefore \angle RTS=50\end{array}$

Thus, $\overline{TR}\cong \overline{TR}\left(\text{common}\text{side}\right)$ and $\angle PTS\cong \angle RTS,\angle TPS\cong \angle TSR$

By ASA theorem, the given triangles are congruent.

Hence, $\Delta TPR\cong \Delta TSR$ .