Chapter 4.7, Problem 4ST3

To determine

To prove:it deduces that $\overrightarrow{KZ}$ bisects $\angle LKJ$

Explanation of Solution

Given information:

System given: $ZL=ZJ$

Calculation:

Considering the figure given

  

Consider the triangle $\text{Δ}LKJ$

It is given that, $ZL=ZJ$

Deduce that $\overrightarrow{KZ}$ bisects $\angle LKJ$

If a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle.

  $ZL=ZJ$

Therefore, point $Z$ is equidistant from the sides of $\angle LKJ$ and $Z$ lies on the bisector of $\angle LKJ$ or $\overrightarrow{KZ}\text{ bisects }\angle LKJ$

Hence, it deduce that $\overrightarrow{KZ}$ bisects $\angle LKJ$