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.)
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