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 of AB is true. Select all statements that must be true.A: AM=BMB: CM = DMC: EA=EMD: EA BM

Answer 1

ANSWER and EXPLANATION

We have that CD is a bisector of AB. This means that it divides AB into two equal parts.

M lies on CD.

E is placed at a point equidistant to A and M. That means that the distance from A to E is the same as M to E

=> AM = BM

This is true since M lies on CD. That means it is equidistant from A and B.

=> CD = DM

This is true because M also lies at a point that is equidistant to point C and D.

=> EA = EM

This is true because as stated earlier, E is placed at a point equidistant to A and M.

=> EA < EB

This is true since E is closer to A than it is to B. So the distance from E to A is less than that from E to B.

=> AM < AB

This is true because AM is shorter than AB as the diagram shows.

=> AM > BM

This is false because we have shown that AM is in fact equal to BM.