Perpendicular Bisector Theorem
Any point on the perpendicular bisector (red line) of AB will be equidistant from A and B.
Formal Proof
Statements Reasons
1. the red line is the perpendicular bisector of AB 1. Given
2. AM=MB 2. def of perp bisector
3. <AMD=90=<BMD 3. def of perp bisector
4.DM=DM 4. reflexive property
5. triangle AMD = triangle BMD 5. SAS
6. AD=BD 6. CPCTC