# Lesson 2

Constructing Patterns

### Problem 1

This diagram was created by starting with points \(A\) and \(B\) and using only straightedge and compass to construct the rest. All steps of the construction are visible. Describe precisely the straightedge and compass moves required to construct the line \(CD\) in this diagram.

### Solution

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### Problem 2

In the construction, \(A\) is the center of one circle, and \(B\) is the center of the other. Identify **all** segments that have the same length as segment \(AB\).

segment \(AC\)

segment \(AE\)

segment \(BC\)

segment \(CD\)

segment \(DE\)

### Solution

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### Problem 3

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 \(AB\).

\(AB\)

\(AC\)

\(BC\)

\(BD\)

\(CD\)

### Solution

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(From Unit 1, Lesson 1.)### Problem 4

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?

\(AB=CD\)

\(AB=CE\)

\(AB=CF\)

\(AB=EF\)

### Solution

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(From Unit 1, Lesson 1.)