Question

1. this diagram is a straightedge and compass construction. a is the center of one circle, and b is the center of the other. a. name a pair of perpendicular line segments. b. name a pair of line segments with the same length.

Explanation:

Step1: Identify perpendicular line - segments

Perpendicular line - segments form a 90 - degree angle. In the diagram, $\overline{AB}$ and the horizontal line passing through $M$ are perpendicular.

Step2: Identify line - segments of equal length

Line - segments of equal length can be found by looking at symmetric parts. $\overline{AM}$ and $\overline{BM}$ are of equal length as they are radii of the same semi - circle.

Answer:

a. $\overline{AB}$ and the horizontal line through $M$ are a pair of perpendicular line segments.
b. $\overline{AM}$ and $\overline{BM}$ are a pair of line segments with the same length.