Question

Complete. You may find that drawing a diagram will help you.

If $\overrightarrow{BX}$is the bisector of $\angle ABC$, then ___?___ role="math" $\cong$___?___.

Short answer

If$\overrightarrow{BX}$ is the bisector of $\angle ABC$, then $\angle ABX\cong \angle CBX$.

Step-by-step solution

Step 1. Definition of Angle bisector.

The ray, that divides an angle into two congruent adjacent angles, is defined as the bisector of an angle.

Step 2. Draw the diagram.

Draw the diagram with ray $\overrightarrow{BX}$bisecting the angle $\angle ABC$.

Step 3. State the conclusion.

From the diagram, it can be clearly concluded that if $\overrightarrow{BX}$is the bisector of $\angle ABC$, then$\overrightarrow{BX}$ will cutwidth="52" height="20" role="math">∠ABC into two equal angles, that is $\angle ABX\cong \angle CBX$.

Therefore, if$\overrightarrow{BX}$ is the bisector of $\angle ABC$, then $\angle ABX\cong \angle CBX$.