Question

$\overrightarrow{\mathrm{UV}}$bisects $\angle \mathbf{WUX}$. Write the theorem that justifies the statement that$\mathbf{V}$ is equidistant from$\overrightarrow{\mathrm{UW}}$ and $\overrightarrow{\mathrm{UX}}$.

Short answer

The theorem that justifies the statement that$V$ is equidistant from$\overrightarrow{UW}$ and$\overrightarrow{UX}$ isthe theorem 4-7 which states that if a point lies on the bisector of the angle then the point is equidistant from the sides of the angle.

Step-by-step solution

Step 1. Observe the diagram.

The diagram showing that $\overrightarrow{UV}$bisects $\angle WUX$is:

Step 2. Write the theorem 4-7.

The theorem 4-7 states that if a point lies on the bisector of the angle then the point is equidistant from the sides of the angle.

Step 3. Description of step.

It is being given that$\overrightarrow{UV}$ bisects $\angle WUX$.

Therefore, the $\overrightarrow{UV}$is the bisector of the angle $\angle WUX$.

Therefore, by using the theorem 4-7 it can be noticed that the point$V$is equidistant from the sides of the angle.

Therefore, the theorem that justifies the statement that $V$is equidistant from $\overrightarrow{UW}$and $\overrightarrow{UX}$is the theorem 4-7 which states that if a point lies on the bisector of the angle then the point is equidistant from the sides of the angle.