Construction Techniques 4: Parallel and Perpendicular Lines

ID: mofup-tulij
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Construction Techniques 4: Parallel and Perpendicular Lines

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Problem 1

1) Which of the following constructions would help to construct a line passing through point CC that is perpendicular to the line ABAB?

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a) Construction of an equilateral triangle with one side AB \text{Construction of an equilateral triangle with one side } AB \text{ }b) Construction of a hexagon with one side BC \text{Construction of a hexagon with one side } BC \text{ }c) Construction of a perpendicular bisector through C \text{Construction of a perpendicular bisector through } C \text{ }d) Construction of a square with one side AB\text{Construction of a square with one side } AB
Problem 2

2) Two distinct lines, ll and mm, are each perpendicular to the same line nn. Select all the true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) Lines ll and mm are perpendicular \quad\quad b) Lines ll and nn are perpendicular. \quad\quad c) Lines mm and nn are perpendicular.

d) Lines ll and mm are parallel. \quad\quad e) Lines ll and nn are parallel. \quad\quad f) Lines mm and nn are parallel.

Problem 3

3) This diagram is a straightedge and compass construction of the bisector of angle BACBAC. Only angle BACBAC is given. Explain the steps of the construction in order. Include a step for each new circle, line, and point.

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Problem 4

4) This diagram is a straightedge and compass construction of a line perpendicular to line ABAB passing through point CC. Which segment has the same length as segment EAEA?

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a) EC  EC \text{ }b) ED  ED \text{ }c) BE  BE \text{ }d) BD BD
Problem 5

This diagram is a straightedge and compass construction.

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5) Which triangle is equilateral?

6) Explain how you know.

Problem 6

7) In the construction, AA is the center of one circle, and BB is the center of the other. Name the segments in the diagram that have the same length as segment ABAB.

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Problem 7

This diagram is a straightedge and compass construction. AA is the center of one circle, and BB is the center of the other.

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8) Name a pair of perpendicular line segments.

9) Name a pair of line segments with the same length.

Problem 8

10) AA, BB, and CC are the centers of the 3 circles. Select all the segments that are congruent to ABAB. Write each corresponding letter in the answer box and separate letters with commas.

a) HFHF \quad\quad b) HAHA \quad\quad c) CECE \quad\quad d) CDCD \quad\quad e) BDBD \quad\quad f) BFBF

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