Lesson 2

Constructing Patterns

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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.

Two circles, centered at A and B, each pass through the center of the other. There is a vertical line segment between their intersection points, labeled C and D.

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 \(AB\).

A diagram of circles and line segments.
A:

segment \(AC\)

B:

segment \(AE\)

C:

segment \(BC\)

D:

segment \(CD\)

E:

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 \(AB\).

Two intersecting circles.
A:

\(AB\)

B:

\(AC\)

C:

\(BC\)

D:

\(BD\)

E:

\(CD\)

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?

Line segments AB and CF are drawn with the same length. Circle with center C passes through point F. Point D lies inside the circle and point E lies outside the circle. Points C, F, and E are collinear.
A:

\(AB=CD\)

B:

\(AB=CE\)

C:

\(AB=CF\)

D:

\(AB=EF\)

Solution

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(From Unit 1, Lesson 1.)