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 $$AB$$.

A:

segment $$AC$$

B:

segment $$AE$$

C:

segment $$BC$$

D:

segment $$CD$$

E:

segment $$DE$$

Solution

For access, consult one of our IM Certified Partners.

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 $$AB$$.

A:

$$AB$$

B:

$$AC$$

C:

$$BC$$

D:

$$BD$$

E:

$$CD$$

Solution

For access, consult one of our IM Certified Partners.

(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?

A:

$$AB=CD$$

B:

$$AB=CE$$

C:

$$AB=CF$$

D:

$$AB=EF$$

Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 1.)