#### Answer

1. We are told that all sides of both triangles are equal. Thus, by the side-side-side congruency theorem, ABC is congruent to ABD.
2. Since this is the case, it follows that the only way for a line to go through both point C and Point D is for it to be a perpendicular bisector.
3. By the definition of perpendicular bisector, AM and MB are congruent, and CD is perpendicular to AB.