Question

you are working on a proof. you know that a and b are on the perpendicular bisector of cd. what can you conclude?
a ac = bd
b cb = ad
c ac = ad
d ab = cd

Explanation:

Step1: Recall the perpendicular bisector theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Since \(A\) is on the perpendicular bisector of \(\overline{CD}\), then \(AC = AD\).
Since \(B\) is on the perpendicular bisector of \(\overline{CD}\), then \(BC=BD\).

Answer:

\(C\) (because \(AC = AD\) by the perpendicular bisector theorem)