Chapter 4.7, Problem 5ST3

To determine

To write: the theorem that justifies the statement that $V$ is equidistant from $\overrightarrow{UW}$ and $\overrightarrow{UX}$ .

Answer to Problem 5ST3

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

Explanation of Solution

Given information:

  $\overrightarrow{UV}$ bisects $\angle WUX$ .

  

Calculation:

Consider the following data:

  $\overrightarrow{UV}$ bisects $\angle WUX$

Since, $\overrightarrow{UV}$ bisects $\angle WUX$ , then $V$ is equidistant from $\overrightarrow{UW}$ and $\overrightarrow{UX}$

The theorem used is as follows:

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

Here point $V$ lies on the bisector of $\angle WUX$ , then $V$ is equidistant from the sides $\overrightarrow{UW}$ and $\overrightarrow{UX}$ of $\angle WUX$ .