Question

1. why is cp in the picture below not a perpendicular bisector? cp is congruent to pb. c is equidistant from a and b. ap is not congruent to pb. ∠cpb is a right angle.

Explanation:

Step1: Recall definition of perpendicular bisector

A perpendicular bisector of a line - segment divides the line - segment into two equal parts (bisects it) and is perpendicular to it.

Step2: Analyze given line \(\overline{CP}\)

In the figure, for \(\overline{CP}\) to be a perpendicular bisector of \(\overline{AB}\), it should bisect \(\overline{AB}\) (i.e., \(AP = PB\)) and be perpendicular to \(\overline{AB}\). We see that \(\angle CPB\) is a right - angle, but \(AP
eq PB\) as there are no congruence marks indicating \(AP = PB\).

Answer:

C. \(\overline{AP}\) is not congruent to \(\overline{PB}\)