Chapter 5.3, Problem 4PSA

To determine

To Prove: $△NPR\text{is isosceles triangle}\text{.}$ .

Explanation of Solution

Given:

  

  $\begin{array}{l}\angle 5\cong \angle 6\\ \overline{RS}\parallel \overline{NP}\end{array}$

Concept Used:

When parallel lines is intersected by a transversal corresponding angles are equal. Sum of linear pairs of angles is $180°$ .

Proof:

  $\begin{array}{l}\text{When parallel lines is intersected by a transversal corresponding angles are equal}\text{. }\\ \because \overline{RS}\parallel \overline{NP}\\ \Rightarrow \angle P=\angle 6\\ \Rightarrow \angle N=\angle 5\\ \text{Here, }\angle 5\cong \angle 6\\ \Rightarrow \angle N\cong \angle P\\ \Rightarrow △NPR\text{is isosceles triangle}\text{.}\end{array}$