Exercise 1 Page 538

If CD is the perpendicular bisector of AB, two things have to be true.

1. CD has to bisect AB.
2. CD has to form a right angle with AB.

To prove this, we can think of the arcs as parts of two circles with A and B as midpoints and with identical radius. Therefore, if we draw AC, BC, AD, and BD, these segments will be congruent.

Examining the diagram, we see △ ABC and △ ABD. Since they both have a pair of congruent sides, they are isosceles triangles where C and D are the vertex angles of the triangles.

When drawing the height from the vertex angle of an isosceles triangle, it will bisect the base and intersect it at a right angle.

Therefore, we know that CD is the perpendicular bisector of AB.