Question

Name the definition, postulate or theorem that justifies the statement.

If bisects $\overrightarrow{\mathrm{SW}}$, $\angle \mathbf{VST}$then $\angle \mathbf{VSW}\cong \angle \mathbf{WST}$.

Short answer

The theorem that justifies the statement is the angle bisector theorem which states that if $\overrightarrow{\mathrm{BX}}$is the bisector of$\angle \mathbf{ABC}$, then $\mathbf{m}\angle \mathbf{ABX}\mathbf{=}\frac{1}{2}\mathbf{m}\angle \mathbf{ABC}$, $\mathbf{m}\angle \mathbf{XBC}\mathbf{=}\frac{1}{2}\mathbf{m}\angle \mathbf{ABC}$and $\angle \mathbf{ABX}\cong \angle \mathbf{XBC}$.

Step-by-step solution

Step 1. Write the angle bisector theorem.

The angle bisector theorem states that if $\overrightarrow{\mathrm{BX}}$is the bisector of $\angle \mathbf{ABC}$, then $\mathbf{m}\angle \mathbf{ABX}\mathbf{=}\frac{1}{2}\mathbf{m}\angle \mathbf{ABC}$,$\mathbf{m}\angle \mathbf{XBC}\mathbf{=}\frac{1}{2}\mathbf{m}\angle \mathbf{ABC}$and $\angle \mathbf{ABX}\cong \angle \mathbf{XBC}$.

Step 2. Description of step.

It is being given that if$\overrightarrow{SW}$bisects role="math" localid="1646593985453" $\angle \mathrm{VST}$, therefore by using the angle bisector theorem it can be said that $\angle \mathrm{VSW}\cong \angle \mathrm{WST}$.

Step 3. Write the theorem that justifies the statement.

The theorem that justifies the statement is the angle bisector theorem which states that if $\overrightarrow{BX}$is the bisector of $\angle ABC$, then $m\angle ABX=\frac{1}{2}m\angle ABC$, $m\angle XBC=\frac{1}{2}m\angle ABC$and $\angle ABX\cong \angle XBC$.