Construction Techniques 1: Perpendicular Bisectors

ID: sohoh-hiris
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Construction Techniques 1: Perpendicular Bisectors

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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. Select all the true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) Line CDCD is perpendicular to segment ABAB \quad\quad b) Point MM is the midpoint of segment ABAB

c) The length ABAB is equal to the length CDCD \quad\quad d) Segment AMAM is perpendicular to segment BMBM

e) CB+BD>CDCB + BD > CD

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Problem 2

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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2) Is point EE closer to point AA, closer to point BB, or the same distance between the points?

3) Explain how you know.

Problem 3

4) Starting with 2 marked points, AA and BB, precisely describe the straightedge and compass moves required to construct the triangle ABCABC in this diagram.

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Problem 4

5) This diagram was created by starting with points CC and DD and using only straightedge and compass to construct the rest. All steps of the construction are visible. Select all the steps needed to produce this diagram. Write each corresponding letter in the answer box and separate letters with commas.

a) Construct a circle centered at AA. \quad\quad b) Construct a circle centered at CC.

c) Construct a circle centered at DD. \quad\quad d) Label the intersection points of the circles AA and BB.

e) Draw the line through points CC and DD. \quad\quad f) Draw the line through points AA and BB.

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Problem 5

6) 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 true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) AB=BCAB = BC \quad\quad b) AB=BDAB = BD \quad\quad c) \quad\quad AD=2ACAD = 2AC \quad\quad d) BC=CDBC = CD \quad\quad e) BD=CDBD = CD

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