Based on the given information, it is guaranteed that ab is perpendicular to cd

False

Step-by-step explanation:

Given AC is equal to BC, the bisector which is also perpendicular to AB includes point C .

In the case that D is the midpoint of segment AB, all the points in CD are at the same distance from A and B, then CD is the perpendicular bisector of AB. But, with the given information D could or could not be the midpoint of segment AB, so it is not guaranteed that AB is perpendicular to CD.