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

Question

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

(Select all that apply.)
Angle DMA= Angle DMB
Segment AB= Segment CD
Segment CM= Segment DM
Angle BDM= Angle CMA
Segment AM= Segment BM

Answer 1

Given that CD is a perpendicular bisector of AB and they intersect at point M, we can analyze the statements provided.

1. Angle DMA = Angle DMB: This statement is true. Since CD is the perpendicular bisector, it means that angle DMB is 90 degrees and angle DMA is 90 degrees, hence they are equal.

2. Segment AB = Segment CD: This statement is not necessarily true. AB may have a different length compared to CD.

3. Segment CM = Segment DM: This statement is not true. The positions of points C and D relative to point M would not guarantee that these segments are equal.

4. Angle BDM = Angle CMA: This statement is true. Because CD is a perpendicular bisector, it creates a symmetry in angles at point M, meaning angle BDM is equal to angle CMA.

5. Segment AM = Segment BM: This statement is also true. By definition of a perpendicular bisector, it bisects segment AB, which means AM is equal to BM.

Thus, the two statements that must be true are:

• Angle DMA = Angle DMB
• Segment AM = Segment BM

So the correct answers are:

• Angle DMA = Angle DMB
• Segment AM = Segment BM