Answer:
2. Definition of the perpendicular bisector
5. Reflexive property of congruence
11. Definition of square root
Step-by-step explanation:
First, we know that CD is a perpendicular bisector of AB. It means that CD crosses AB at an angle of 90 degrees and the point of intersection is the midpoint of AB.
Therefore, we can say that D is the midpoint of AB because it is the definition of a perpendicular bisector.
We also can say that CD = CD by the reflexive property of congruence that says that a segment is equal to itself.
Finally, from (BC)² = (AC)², we can say that BC = AC, because we can apply the square root to both sides and it doesn't change the equality.
Therefore, the answers are:
Reasons:
2. Definition of the perpendicular bisector
5. Reflexive property of congruence
11. Definition of square root