Question

1. 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 = bm
b. cm = dm
c. ea = em
d. ea < eb
e. am < ab
f. am > bm

Explanation:

Step1: Recall property of perpendicular bisector

Since \(CD\) is the perpendicular bisector of \(AB\), by the definition of a bisector, it divides \(AB\) into two equal - length segments. So \(AM = BM\).

Step2: Analyze segment - length relationships

\(AM\) is half of \(AB\) (because \(M\) is the mid - point of \(AB\)), so \(AM

Step3: Analyze other options

There is no information given to suggest that \(CM = DM\) (we only know about the perpendicular bisector of \(AB\), not \(CD\)), \(EA = EM\) (no reason for point \(E\) to have this property), \(EABM\) is wrong as \(AM = BM\).

Answer:

A. \(AM = BM\)
E. \(AM