Question

write a true biconditional about angle bisectors. select the correct choices below so that the resulting sentence is a true biconditional about angle bisectors. dropdown is the bisector of dropdown if and only if dropdown

Explanation:

Step1: Recall the definition of an angle bisector

An angle bisector is a ray that divides an angle into two congruent adjacent angles. So, for angle \( \angle ABC \) with bisector \( \overrightarrow{BX} \), the ray \( \overrightarrow{BX} \) is the bisector of \( \angle ABC \) if and only if \( \angle ABX \cong \angle CBX \) (or \( m\angle ABX = m\angle CBX \)).

Step2: Fill in the blanks

From the diagram, the ray is \( \overrightarrow{BX} \), the angle is \( \angle ABC \), and the condition is that it divides the angle into two equal (congruent) angles, i.e., \( m\angle ABX = m\angle CBX \) (or \( \angle ABX \cong \angle CBX \)).

Answer:

\( \boldsymbol{\overrightarrow{BX}} \) is the bisector of \( \boldsymbol{\angle ABC} \) if and only if \( \boldsymbol{m\angle ABX = m\angle CBX} \) (or \( \boldsymbol{\angle ABX \cong \angle CBX} \))