Chapter 3.4, Problem 2PSA

To determine

The line segment $\overrightarrow{MJ}$ bisects $\angle HMK$ .

Explanation of Solution

Given information : In this question, we have given that $\overline{HJ}\cong \overline{KJ}$ and $\angle MJH\cong \angle MJK$

Formula used: SAS Congruency rule.

Proof: In $\Delta MJH$ and $\Delta MJK$

  $\overline{HJ}\cong \overline{KJ}$ (Given)

  $\angle MJH\cong \angle MJK$ (Given)

  $\overline{MJ}\cong \overline{MJ}$ (Common)

  $\therefore \Delta MJH\cong \Delta MJK$ (BY SAS Congruency rule)

  $\Rightarrow \angle JMH\cong \angle JMK$ (BY CPCT)

  $\therefore$ $\overrightarrow{MJ}$ bisects $\angle HMK$ .