Question

In this diagram, line segment CD is the perpendicular bisector of line segment AB. Assume the conjecture that the set of points equidistant from A and B is the perpendicular bisector AB is true. Select all statements that must be true.

Answer Choices:
AM=BM
CM=DM
EA=EM
EA BM

Answer 1

Option (2)

Explanation:

Conjecture of the perpendicular bisector of a segment clearly states that,

"If a point is on the perpendicular bisector of a segment then it is equidistant from the endpoints of the segment".

From the figure attached,

CD is the perpendicular bisector of line segment AB.

By the conjecture, M is a point lying on perpendicular bisector CD,

Therefore, CM = DM will be the answer.

Option (2) will be the correct option.