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 $overline{de}$
it must be the same length as segment $overline{bc}$
it must be the same length as segment $overline{ab}$
it must be the same length as segment $overline{ea}$

Explanation:

A perpendicular bisector divides a line - segment into two equal - length segments. Since $\overline{AC}$ is the perpendicular bisector of $\overline{BD}$ and they meet at point $E$, by the definition of a perpendicular bisector, $E$ is the mid - point of $\overline{BD}$. So, $\overline{BE}$ and $\overline{DE}$ have the same length.

Answer:

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