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: Recall perpendicular lines property

Perpendicular lines form 90 - degree angles. In a straight - edge and compass construction of two intersecting circles, the line joining the centers and the common chord are perpendicular.

Step2: Recall equal - length line segments property

Radii of the same circle are equal. Also, in symmetric constructions like this, some other segments can be equal.

Answer:

a. $\overline{AB}$ and $\overline{CD}$
b. $\overline{AC}$ and $\overline{AD}$ (or $\overline{BC}$ and $\overline{BD}$, or $\overline{AM}$ and $\overline{BM}$)