Question

julia is using this figure to prove that triangle abc is an isosceles triangle. first, she used the converse of the perpendicular bisector theorem and the definition of perpendicular lines to determine that ce is the perpendicular bisector of ab. what could be the next step of a valid proof? a. ae = ce because of the perpendicular bisector theorem b. ce = bc because of the perpendicular bisector theorem c. ac = bc because of the perpendicular bisector theorem d. ce = ab because of the perpendicular bisector theorem

Explanation:

Step1: Recall perpendicular bisector theorem

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In \(\triangle ABC\), \(CE\) is the perpendicular bisector of \(AB\). The endpoints of segment \(AB\) are \(A\) and \(B\), and point \(C\) lies on the perpendicular bisector \(CE\).

Step2: Apply the theorem

By the perpendicular - bisector theorem, since \(C\) is on the perpendicular bisector of \(AB\), we have \(AC = BC\).

Answer:

C. \(AC = BC\) because of the perpendicular bisector theorem