Construction Techniques 4: Parallel and Perpendicular Lines

ID: mofup-tulij
Illustrative Math
Subject: Geometry

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 ﻿$C$﻿ that is perpendicular to the line ﻿$AB$﻿?

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

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

a) Lines ﻿$l$﻿ and ﻿$m$﻿ are perpendicular ﻿$\quad\quad$﻿ b) Lines ﻿$l$﻿ and ﻿$n$﻿ are perpendicular. ﻿$\quad\quad$﻿ c) Lines ﻿$m$﻿ and ﻿$n$﻿ are perpendicular.

d) Lines ﻿$l$﻿ and ﻿$m$﻿ are parallel. ﻿$\quad\quad$﻿ e) Lines ﻿$l$﻿ and ﻿$n$﻿ are parallel. ﻿$\quad\quad$﻿ f) Lines ﻿$m$﻿ and ﻿$n$﻿ are parallel.

Problem 3

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

Problem 4

4) This diagram is a straightedge and compass construction of a line perpendicular to line ﻿$AB$﻿ passing through point ﻿$C$﻿. Which segment has the same length as segment ﻿$EA$﻿?

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

This diagram is a straightedge and compass construction.

5) Which triangle is equilateral?

6) Explain how you know.

Problem 6

7) In the construction, ﻿$A$﻿ is the center of one circle, and ﻿$B$﻿ is the center of the other. Name the segments in the diagram that have the same length as segment ﻿$AB$﻿.

Problem 7

This diagram is a straightedge and compass construction. ﻿$A$﻿ is the center of one circle, and ﻿$B$﻿ is the center of the other.

8) Name a pair of perpendicular line segments.

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

Problem 8

10) ﻿$A$﻿, ﻿$B$﻿, and ﻿$C$﻿ are the centers of the 3 circles. Select all the segments that are congruent to ﻿$AB$﻿. Write each corresponding letter in the answer box and separate letters with commas.

a) ﻿$HF$﻿ ﻿$\quad\quad$﻿ b) ﻿$HA$﻿ ﻿$\quad\quad$﻿ c) ﻿$CE$﻿ ﻿$\quad\quad$﻿ d) ﻿$CD$﻿ ﻿$\quad\quad$﻿ e) ﻿$BD$﻿ ﻿$\quad\quad$﻿ f) ﻿$BF$﻿