Constructing Patterns

ID: lumun-jagof
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Constructing Patterns

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Problem 1

1) This diagram was created by starting with points AA and BB 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 CDCD in this diagram.

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Problem 2

2) In the construction, AA is the center of one circle, and BB is the center of the other. Identify all segments that have the same length as segment ABAB. Write each corresponding letter in the answer box and separate letters with commas.

a) segment ACAC \quad\quad b) segment AEAE \quad\quad c) segment BCBC \quad\quad d) segment CDCD \quad\quad e) segment DEDE

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Problem 3

3) This diagram was constructed with straightedge and compass tools. AA is the center of one circle, and CC is the center of the other. Select all line segments that must have the same length as segment ABAB. Write each corresponding letter in the answer box and separate letters with commas.

a) ABAB \quad\quad b) ACAC \quad\quad c) BCBC \quad\quad d) BDBD \quad\quad e) CDCD

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Problem 4

4) Clare used a compass to make a circle with a radius the same length as segment ABAB. She labeled the center CC. Which statement must be true?

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a) AB=CD AB = CD b) AB=CE AB = CE c) AB=CF AB = CF d) AB=EF AB = EF