Question

given: m∠aeb = 45° ∠aec is a right angle. prove: (overrightarrow{eb}) bisects ∠aec. proof: we are given that m∠aeb = 45° and ∠aec is a right angle. the measure of ∠aec is 90° by the definition of a right angle. applying the drop - down options: segment addition property, angle addition postulate, reflexive property, transitive property gives m∠aeb the substitution property subtraction property 5°, so have the same measure. congruent angles, it is

Explanation:

Step1: Recall angle - related properties

We know that $\angle AEC$ is a right - angle, so $m\angle AEC = 90^{\circ}$. We are given $m\angle AEB=45^{\circ}$.

Step2: Use the angle addition postulate

By the angle addition postulate, $\angle AEC=\angle AEB+\angle BEC$. Since $m\angle AEC = 90^{\circ}$ and $m\angle AEB = 45^{\circ}$, then $m\angle BEC=m\angle AEC - m\angle AEB=90^{\circ}-45^{\circ}=45^{\circ}$.

Step3: Determine the bisector

Since $m\angle AEB = m\angle BEC = 45^{\circ}$, $\overrightarrow{EB}$ bisects $\angle AEC$. The property used to find the measure of $\angle BEC$ based on the relationship between $\angle AEC$ and $\angle AEB$ is the angle addition postulate.

Answer:

angle addition postulate