Question

proofs about angles quick check
line segment $overline{ac}$ is a perpendicular bisector of segment $overline{bd}$, with the two segments meeting at point $e$. what is true of segment $overline{be}$? (1 point)
it must be the same length as segment $overline{ab}$.
it must be the same length as segment $overline{ea}$.
it must be the same length as segment $overline{de}$.
it must be the same length as segment $overline{bc}$.

Explanation:

Step1: Recall definition of bisector

A bisector of a line - segment divides it into two equal - length segments.

Step2: Apply to given problem

Since $\overline{AC}$ is the bisector of $\overline{BD}$ and they meet at point $E$, by the definition of a bisector, $BE = DE$.

Answer:

It must be the same length as segment $\overline{DE}$.