Question

jonas constructed a perpendicular bisector as shown. which statements are true? select all that apply. a it is perpendicular to ab. b it divides ab into two congruent line segments. c it is exactly the same length as ab. d the distance from a to any point on the bisector is equal distance from b to the same point on the bisector.

Explanation:

Step1: Recall properties of perpendicular bisector

A perpendicular bisector of a line - segment $\overline{AB}$ is perpendicular to $\overline{AB}$ and divides $\overline{AB}$ into two congruent line - segments. Also, any point on the perpendicular bisector of a line - segment is equidistant from the endpoints of the line - segment.

Step2: Analyze each statement

• Statement A: A perpendicular bisector of $\overline{AB}$ is perpendicular to $\overline{AB}$. This is a fundamental property of a perpendicular bisector.
• Statement B: A perpendicular bisector of $\overline{AB}$ divides $\overline{AB}$ into two congruent line - segments. This is also a basic property.
• Statement D: The distance from any point on the perpendicular bisector of $\overline{AB}$ to $A$ is equal to the distance from that point to $B$. This is based on the definition of a perpendicular bisector as the set of points equidistant from $A$ and $B$.
• Statement C: A perpendicular bisector of $\overline{AB}$ is not necessarily exactly the same length as $\overline{AB}$. A perpendicular bisector is a line, and a line - segment has a finite length, and there is no such length - equality relationship in general.

Answer:

A. It is perpendicular to $\overline{AB}$, B. It divides $\overline{AB}$ into two congruent line segments, D. The distance from any point on the bisector to $A$ is equal to the distance from the same point to $B$