Question

1. is \\(\overline{cp}\\) a perpendicular bisector of \\(\overline{ab}\\)? explain your answer.

Explanation:

A perpendicular bisector must satisfy two conditions: 1) it intersects the segment at a right angle, and 2) it divides the segment into two congruent (equal-length) parts. While $\overline{CP}$ forms a right angle with $\overline{AB}$ (shown by the right angle symbol), the tick marks show that $PB$ is congruent to the segment from $P$ to the marked point on $AB$, not that $AP = PB$. This means $P$ is not the midpoint of $\overline{AB}$.

Answer:

No, $\overline{CP}$ is not a perpendicular bisector of $\overline{AB}$. Although $\overline{CP}$ is perpendicular to $\overline{AB}$, it does not bisect $\overline{AB}$ (point $P$ is not the midpoint of $\overline{AB}$ as shown by the unequal segment markings).