Question

1. why is $overline{cp}$ in the picture below not a perpendicular bisector?

$angle cpb$ is a right angle.
$overline{ap}$ is not congruent to $overline{pb}$.
$overline{cp}$ is congruent to $overline{pb}$.
c is equidistant from a and b.

Explanation:

Step1: Recall perpendicular - bisector definition

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

Step2: Analyze the given line segment \(AB\) and line \(CP\)

In the figure, for \(\overline{CP}\) to be a perpendicular bisector of \(\overline{AB}\), it must be perpendicular to \(\overline{AB}\) and \(AP = PB\). We see that \(\angle CPB\) is a right - angle, so \(\overline{CP}\) is perpendicular to \(\overline{AB}\). But from the markings, \(\overline{AP}\) is not congruent to \(\overline{PB}\).

Answer:

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