Question

júlia 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 (overline{ce}) is the perpendicular bisector of (overline{ab}). what could be the next step of a valid proof? a. (ae = ce) because of the perpendicular bisector theorem b. (ac = bc) because of the perpendicular bisector theorem c. (ce = ab) because of the perpendicular bisector theorem d. (ce = bc) because of the perpendicular bisector theorem

Explanation:

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. Since \(CE\) is the perpendicular bisector of \(AB\), point \(C\) is on the perpendicular bisector of \(AB\). So, by the perpendicular bisector theorem, \(AC = BC\).

Answer:

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