Question

1. clare used a compass to make a circle with radius the same length as segment ab. she labeled the center c. which statement must be true? a. ab = cd b. ab = ce c. ab = cf d. ab = ef why? explain.

Explanation:

Step1: Recall the definition of a circle's radius

The radius of a circle is the distance from the center of the circle to any point on the circle.

Step2: Identify the radius - related segments

Segment \(AB\) is used to set the radius of the circle. Points \(C\) is the center of the circle. Segments \(CD\), \(CE\), \(CF\) are all radii of the circle as they connect the center \(C\) to points on the circle (\(D\), \(E\), \(F\) respectively).

Step3: Compare the lengths

Since the circle is made with radius the same length as segment \(AB\), and \(CD\), \(CE\), \(CF\) are radii of the circle, we have \(AB = CD=CE = CF\).

Answer:

A. \(AB = CD\), B. \(AB = CE\), C. \(AB = CF\)