Question

1. this diagram was constructed with straightedge and compass tools. a is the center of one circle, and c is the center of the other. select all line segments that must have the same length as segment ab.

a. ab
b. ac
c. bc
d. bd
e. cd
(from unit 1, lesson 1.)

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
(from unit 1, lesson 1.)

Explanation:

Step1: Recall radius property

In a circle, all radii are equal. In the first - part, if \(A\) is the center of a circle and \(AB\) is a radius of the circle centered at \(A\), then any other radius of the circle centered at \(A\) has the same length as \(AB\). There is no information suggesting that \(AC\), \(BC\), \(BD\), or \(CD\) are radii of the circle centered at \(A\). So, the only segment with the same length as \(AB\) is \(AB\) itself (since we are looking for segments equal to \(AB\)).

Step2: Analyze second - part

Clare made a circle with center \(C\) and radius equal to the length of \(AB\). In the circle with center \(C\), all radii of this circle are equal to the radius of the circle. So, if \(AB\) is equal to the radius of the circle centered at \(C\), and \(CF\) is a radius of the circle centered at \(C\), then \(AB = CF\).

Answer:

1. A. \(AB\)
2. C. \(AB = CF\)