Chapter 3.3, Problem 14PSB

To determine

To prove : The congruency of $\angle J$ with respect to $\angle P$ .

Explanation of Solution

Given information : In this question, we have given that $\angle 5\cong \angle 6$ , $\angle JHG\cong \angle O$ and $\overline{GH}\cong \overline{MO}$

Formula used: ASA Congruency rule.

Proof: $\angle JGH+\angle 5\cong 90°$ and $\angle PMO+\angle 6\cong 90°$

  $\Rightarrow \angle JGH=90°-\angle 5$ and $\angle PMO=90°-\angle 6$

As, $\angle 5\cong \angle 6$ ,

  $\Rightarrow \angle JGH=90°-\angle 5$ and $\angle PMO=90°-\angle 5$

  $\therefore \angle JGH\cong \angle PMO$

Now, In $\Delta JGH$ and $\Delta PMO$

  $\angle JGH\cong \angle PMO$ (Proved above)

  $\overline{GH}\cong \overline{MO}$ (Given)

  $\angle JHG\cong \angle O$ (Given)

  $\therefore \Delta JGH\cong \Delta PMO$ (BY ASA Congruency rule)

  $\Rightarrow \angle J\cong \angle P$ (BY CPCT)