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:

1.

Step1: Recall circle - radius property

In a circle, all radii are equal. In the given construction, in the circle with center \(B\), \(AB\) and \(BD\) are both radii of the circle centered at \(B\).

Step2: Apply radius - equality

Since all radii of a circle have the same length, and \(AB\) and \(BD\) are radii of the circle centered at \(B\), we can conclude that \(AB = BD\).

2.

Clare made a circle with radius the same length as segment \(AB\) and labeled the center \(C\). By the definition of a radius of a circle, all radii of a given circle are equal in length. So, if the radius of the circle centered at \(C\) is set to be equal to \(AB\), and \(CD\) is a radius of the circle centered at \(C\), then \(AB = CD\).

Answer:

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