Question

unit 1 lesson 1 cumulative practice problems

1. here is a diagram of a straightedge and compass construction. c is the center of one circle, and b is the center of the other. explain why the length of segment bd is the same as the length of segment ab.
2. clare used a compass to make a circle with radius the same length as segment ab. she labeled the center c. which statement is true?

a. ab > cd
b. ab = cd
c. ab > ce
d. ab = ce

Explanation:

Step1: Recall radius property

The radius of a circle is the distance from the center of the circle to any point on the circle. All radii of a given - circle are equal in length.

Step2: Analyze problem 1

In the first problem, since \(B\) is the center of one circle and \(BD\) and \(AB\) are both radii of the circle with center \(B\), by the definition of a radius, \(BD = AB\).

Step3: Analyze problem 2

Clare made a circle with center \(C\) and radius equal to the length of segment \(AB\). In the circle with center \(C\), \(CD\) and \(CF\) and \(CE\) are all radii of the circle with center \(C\). Since the radius of the circle with center \(C\) is equal to the length of \(AB\), we have \(AB = CD\) (because \(CD\) is a radius of the circle with center \(C\) and the radius of the circle with center \(C\) is set to be equal to \(AB\)).

Answer:

1. The length of segment \(BD\) is the same as the length of segment \(AB\) because \(B\) is the center of the circle and \(AB\) and \(BD\) are both radii of the circle centered at \(B\), and all radii of a circle are equal.
2. B. \(AB = CD\)