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.)
Which of the following statements must be true? Choose two.
(Select all that apply.)
Answers
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Answered by
GPT-4o mini
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:
1. **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.
2. **∠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°.
1. **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.
2. **∠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°.
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