Proofs About Angles Quick Check

Question

4 of 54 of 5 Items

Question
Line segment AC¯¯¯¯¯¯¯¯ is a perpendicular bisector of segment BD¯¯¯¯¯¯¯¯ , with the two segments meeting at point E . What is true of segment BE¯¯¯¯¯¯¯¯ ? (1 point)
Responses

It must be the same length as segment AB¯¯¯¯¯¯¯¯.
It must be the same length as segment upper A upper B .

It must be the same length as segment EA¯¯¯¯¯¯¯¯.
It must be the same length as segment upper C upper D .

It must be the same length as segment BC¯¯¯¯¯¯¯¯.
It must be the same length as segment upper B upper C .

It must be the same length as segment DE¯¯¯¯¯¯¯¯.

Answer 1

If line segment \( AC \) is a perpendicular bisector of segment \( BD \) and they meet at point \( E \), then the following is true:

• By definition of a perpendicular bisector, it divides segment \( BD \) into two equal parts. Therefore, segment \( BE \) must be equal in length to segment \( ED \).

From the options provided, the one that best represents the relationship is:

It must be the same length as segment DE.

So the correct response would be:

It must be the same length as segment DE.