CD is a perpendicular bisector of AB, and they intersect at point M.

Question

CD is a perpendicular bisector of AB, and they intersect at point M.

Which of the following statements must be true? Choose two.

(Select all that apply.)

Answer 1

Based on the fact that CD is a perpendicular bisector of line segment AB and they intersect at point M, we can conclude the following statements must be true:

AM = MB: Since CD is the bisector of AB, it divides AB into two equal parts at point M. Therefore, the lengths of AM and MB are equal.
∠CMD = ∠BMD = 90°: Since CD is perpendicular to AB, the angle formed between line CD and line AB at point M is a right angle. Hence, both angles ∠CMD and ∠BMD are 90 degrees.

So, the two statements that must be true are AM = MB and ∠CMD = ∠BMD = 90°.