Question

1. in the construction, circle q and circle s have the same radius length. identify all segments that have the same length as segment pr.

a. segment pu
b. segment uv
c. segment rw
d. segment rt
e. segment qs

Explanation:

Step1: Recall circle - radius property

In a circle, all radii are equal. Since circle \(Q\) and circle \(S\) have the same radius length.

Step2: Identify radii - like segments

Segment \(PR\) is the distance between the centers of two congruent - radius circles (\(Q\) and \(S\)) which is equal to the sum of their radii. Segment \(QS\) is also the distance between the centers of the two circles, so \(QS = PR\). Also, segment \(RW\) is a radius of circle \(S\) and segment \(PU\) is a radius of circle \(Q\), and the sum of the lengths of two radii (e.g., \(PU + RW\)) is equal to \(PR\) in terms of the geometric relationship of the circles.

Answer:

A. segment \(PU\), C. segment \(RW\), E. segment \(QS\)