Chapter 3, Problem 11RP

To determine

To prove: K and J are correct.

Explanation of Solution

Given information :

Here, we have given that $\overline{PT}$ is congruent to $\overline{TS}$ , $\overline{NT}$ is congruent to $\overline{TR}$ and $\overline{SR}=70$ m.

Proof: In $\Delta PTN$ and $\Delta STR$ ,

  $\overline{PT}\cong \overline{TS}$ (Given)

  $\angle PTN\cong \angle STR$ (Vertically Opposite Angles)

  $\overline{NT}\cong \overline{TR}$ (Given)

  $\Rightarrow \Delta PTN\cong \Delta STR$ (By SAS Congruency Rule)

  $\therefore \overline{PN}\cong \overline{SR}$ (By Corresponding Part of Congruent Triangles)

As, $\overline{SR}=70$ m

  $\Rightarrow \overline{PN}=70$ m

  $\therefore$ K and J are correct