Construction Techniques 3: Perpendicular Lines and Angle Bisectors

ID: ravus-jakit
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Construction Techniques 3: Perpendicular Lines and Angle Bisectors

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Problem 1

1) This diagram is a straightedge and compass construction of a line perpendicular to line ABAB passing through point CC. Explain why it was helpful to construct points DD and AA to be the same distance from CC.

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Problem 2

2) This diagram is a straightedge and compass construction. Select all true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) Line EFEF is the bisector of angle BACBAC. \quad\quad b) Line EFEF is the perpendicular bisector of segment BABA.

c) Line EFEF is the perpendicular bisector of segment ACAC. \quad\quad d) Line EFEF is the perpendicular bisector of segment BDBD.

e) Line EFEF is parallel to line CDCD.

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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. A rhombus is a quadrilateral with 4 congruent sides. Explain why quadrilateral ACBDACBD is a rhombus.

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Problem 4

4) AA, BB, and CC are the centers of the three circles. Which line segment is congruent to HFHF?

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a) AB  AB \text{ }b) CD  CD \text{ }c) DF  DF \text{ }d) CB CB
Problem 5

5) In the construction, AA is the center of one circle, and BB is the center of the other. Explain why segment EAEA is the same length as segment BCBC.

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Problem 6

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.

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6) Is point MM closer to point AA, closer to point BB, or the same distance from both points?

7) Explain how you know.

Problem 7

8) A sheet of paper with points AA and BB is folded so that AA and BB match up with each other.

Explain why the crease in the sheet of paper is the perpendicular bisector of segment ABAB. (Assume the conjecture that the set of points equidistant from AA and BB is the perpendicular bisector of segment ABAB is true.)

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Problem 8

9) Here is a diagram of a straightedge and compass construction. CC is the center of one circle, and BB is the center of the other. Explain why the length of segment CBCB is the same as the length of segment CDCD.

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