Question

Note that $\mathit{Z}\mathit{L}\mathbf{=}\mathit{Z}\mathit{J}$. Can you deduce that$\mathit{K}\mathit{Z}$ bisects $\angle \mathit{L}\mathit{K}\mathit{J}$?

Short answer

It is being given that $\mathit{Z}\mathit{L}\mathbf{=}\mathit{Z}\mathit{J}$.

Therefore, the point$\mathit{Z}$is equidistant from the sides of the angle.

Therefore, by using the theorem 4-8 it can be noticed that the point$\mathit{Z}$lies on the angle bisector of the angle $\angle \mathit{L}\mathit{K}\mathit{J}$.

Therefore, yes, it can be deduced that $\mathit{K}\mathit{Z}$bisects $\angle \mathit{L}\mathit{K}\mathit{J}$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the theorem 4-8.

The theorem 4-8 states that if a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle.

Step 3. Description of step.

It is being given that $ZL\mathbf{=}ZJ$.

Therefore, the point$Z$is equidistant from the sides of the angle.

Therefore, by using the theorem 4-8 it can be noticed that the point$Z$ lies on the angle bisector of the angle $\angle LKJ$.

Therefore, yes, it can be deduced that $KZ$bisects$\angle LKJ$.