Construction Techniques 2: Equilateral Triangles

ID: kogam-gugod
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Construction Techniques 2: Equilateral Triangles

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Problem 1

1) This diagram is a straightedge and compass construction. AA is the center of one circle, and BB is the center of the other. Explain how we know triangle ABCABC is equilateral.

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Problem 2

2) AA,BB,and CC are the centers of the 3 circles. How many equilateral triangles are there in this diagram?

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Problem 3

3) This diagram is a straightedge and compass construction. AA is the center of one circle, and BB is the center of the other. Select all the true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) AC=BCAC=BC \quad\quad b) AC=BDAC=BD \quad\quad c) CD=ABCD=AB \quad\quad d) ABCDABCD is a square. \quad\quad e) ABDABD is an equilateral triangle.

f) CD=AB+ABCD=AB+AB

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Problem 4

4) Line segment CDCD is the perpendicular bisector of line segment ABAB. Is line segment ABAB the perpendicular bisector of line segment CDCD?

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Problem 5

Here are 2 points in the plane.

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5) Using only a straightedge, can you find points in the plane that are the same distance from points AA and BB?

True or false? Write below.

6) Explain your reasoning.

7) Using only a compass, can you find points in the plane that are the same distance from points AA and BB?

True or false? Write below.

8) Explain your reasoning.

Problem 6

9) In this diagram, line segment CDCD is the perpendicular bisector of line segment ABAB. Assume the conjecture that the set of points equidistant from AA and BB is the perpendicular bisector of ABAB is true. Select all statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) AM=BMAM=BM \quad\quad b) CM=DMCM=DM \quad\quad c) EA=EMEA=EM \quad\quad d) EA<EBEA<EB \quad\quad e) AM<ABAM<AB \quad\quad f) AM>BMAM>BM

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Problem 7

10) The diagram was constructed with straightedge and compass tools. Name all segments that have the same length as segment ACAC .

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Problem 8

11) Starting with 2 marked points, AA and BB, precisely describe the straightedge and compass moves required to construct the quadrilateral ACBDACBD in this diagram.

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Problem 9

12) In the construction, AA is the center of one circle and BB is the center of the other. Which segment has the same length as ABAB?

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a) CB  CB \text{ }b) CD  CD \text{ }c) CE  CE \text{ }d) CA CA