Chapter 4.3, Problem 11PSB

To determine

To Prove: $QS\perp PR.$

Explanation of Solution

Given information: $\angle RQT=\angle RST,QT=TS$

Formula used: Congruency of triangles, linear pair axiom.

Calculation:

  $\begin{array}{l}QT=TS,\angle RQT=\angle RST\text{(Given)}\\ RT=RT(\text{Reflective}\text{property})\\ \therefore \Delta RQT\cong \Delta RST(\text{SAS})\\ \therefore \angle RTQ=\angle RTS(\text{CPCT})\\ \angle ETQ+\angle RTS={180}^{\circ }(\text{linear}\text{pair}\text{axiom)}\\ \therefore \angle RTQ={90}^{\circ }=\angle RTS\\ \therefore QS\perp PR.\end{array}$