Question

from unit 1, lesson 3
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:

• Since $CD$ is the perpendicular bisector of $AB$, by the definition of a perpendicular bisector, any point on it is equidistant from $A$ and $B$. So $AM = BM$, making option A true.
• There is no information given to suggest that $CM=DM$ as $CD$ being the perpendicular - bisector of $AB$ does not imply this about the segments on $CD$ itself, so option B is false.
• There is no reason to assume $EA = EM$ just based on the given perpendicular - bisector information, so option C is false.
• Since $E$ is on the perpendicular bisector of $AB$, $EA=EB$, so option D is false.
• $AM$ is half of $AB$ (because $M$ is the mid - point of $AB$), so $AM
• As $M$ is the mid - point of $AB$, $AM = BM$, so option F is false.

Answer:

A. $AM = BM$
E. $AM