Question

1. in this diagram, line segment cd is the perpendicular bisector of line segment ab. assume conjecture that the set of points equidistant from a and b is the perpendicular bisector of ab select all statements that must be true.

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

Explanation:

Step1: Recall the property of perpendicular bisector

A point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Since \(CD\) is the perpendicular bisector of \(AB\), for any point \(M\) on \(CD\), \(AM = BM\).

Step2: Analyze other options

• Option b: There is no information given to suggest \(CM=DM\).
• Option c: There is no basis to claim \(EA = EM\).
• Option d: There is no reason to say \(EA
• Option e: There is no evidence for \(AM < AB\).
• Option f: There is no ground for \(AM>BM\) as \(AM = BM\) from the perpendicular bisector property.

Answer:

a. \(AM = BM\)