Chapter 3, Problem 4RP

To determine

To prove : The congruency of $\overline{PJ}$ with respect to $\overline{MK}$ .

Explanation of Solution

Given information : Here, we have given that $\overline{PJ}$ and $\overline{JM}$ bisect each other at $R$ .

Proof: As, $\overline{PJ}$ and $\overline{JM}$ bisect each other at $R$ ,

  $\Rightarrow \overline{PR}\cong \overline{KR}$ and $\overline{JR}\cong \overline{MR}$

Now, In $\Delta PRJ$ and $\Delta MRK$

  $\overline{PR}\cong \overline{KR}$ (Proved above)

  $\overline{JR}\cong \overline{MR}$ (Proved above)

  $\angle 4\cong \angle 5$ (Vertically Opposite Angles)

  $\Rightarrow \Delta PRJ\cong \Delta MRK$ (By SAS Congruency Rule)

  $\therefore \overline{PJ}\cong \overline{MK}$ (By Corresponding Part of Congruent Triangles)