Chapter 4, Problem 10CR

To determine

Prove $\overline{JK}\cong \overline{LK}$

Explanation of Solution

Given:

  

  $\angle JMK\cong \angle LMK$

  $\overline{MK}\perp$ plane P.

Calculation:

Since $\overline{MK}\perp$ plane P.

So, $\overline{MK}\perp \overline{JK}$ and $\overline{MK}\perp \overline{LK}$

Consider the right angled $\Delta JMK\text{ and }\Delta LMK$ :

  $\angle JMK\cong \angle LMK$

  $\overline{MK}\cong \overline{MK}$

  $\angle MKJ\cong \angle MKL$

So, by ASA Postulate, $\Delta JMK\cong \Delta LMK$ .

So, $\overline{JK}\cong \overline{LK}$ .

Hence proved.