Line segment AC is a perpendicular bisector of segment BD, with the two segments meeting at point E. What is true of segment BE?

Question

A. It must be the same length as a segment EA.
B. it must be the same length as segment AB
C. It must be the same length as segment BC
D. it must be the same length as segment DE

Answer 1

Since line segment AC is the perpendicular bisector of segment BD, it has two important properties:

1. Point E is the midpoint of segment BD, which means that segment BE has the same length as segment ED (BE = ED).
2. Because AC is a perpendicular bisector, it intersects BD at a right angle.

Given that information, let's evaluate the choices:

A. It must be the same length as segment EA. - This is not necessarily true without further information about points A and E.

B. It must be the same length as segment AB. - This is not necessarily true; we have no reason to assume that segments AB and BE are equal.

C. It must be the same length as segment BC. - This is also not necessarily true, as AC does not relate segment BE with BC in this context.

D. It must be the same length as segment DE. - This is true because, as mentioned, E is the midpoint of segment BD (BE = ED).

Therefore, the correct answer is D. It must be the same length as segment DE.