Question

given: $m\angle aeb = 45^{circ}$, $\angle aec$ is a right - angle. prove: $\overrightarrow{eb}$ bisects $\angle aec$. proof: we are given that $m\angle aeb = 45^{circ}$ and $\angle aec$ is a right angle. the measure of $\angle aec$ is $90^{circ}$ by the definition of a right angle. applying the gives $m\angle aeb + m\angle bec = m\angle aec$. segment addition property, angle addition postulate, reflexive property, transitive property gives $45^{circ}+m\angle bec = 90^{circ}$. we need to find $m\angle bec = 45^{circ}$, so $\angle aeb$ and $\angle bec$ have the same measure. since $\overrightarrow{eb}$ divides $\angle aec$ into two congruent angles, it is the angle bisector.

Explanation:

Step1: Identify relevant property

We need to find the property for $m\angle AEB + m\angle BEC=m\angle AEC$.

Step2: Recall angle - related properties

The angle addition postulate states that if point B lies in the interior of $\angle AEC$, then $m\angle AEB + m\angle BEC=m\angle AEC$.

Answer:

angle addition postulate