3-6
Constructing Parallel and
Perpendicular Lines
PART 1
Vocabulary
Review
Write T for true or F for false.
1. A rectangle has two pairs of parallel sides.
2. A rectangle has two pairs of perpendicular sides.
Write alternate exterior, alternate interior, or corresponding to describe
each angle pair.
4.
1
2
5.
4
Vocabulary Builder
construction (noun) kun STRUCK shun
Other Word Forms: construct (verb), constructive (adjective)
Main Idea: Construction means how something is built or constructed.
Math Usage: A construction is a geometric figure drawn using a straightedge
and a compass.
Use Your Vocabulary
6. Complete each statement with the correct form of the word construction.
VERB
You 9 sand castles at the beach.
NOUN
The 9 on the highway caused quite a traffic jam.
ADJECTIVE
The time you spent working on your homework was 9.
Chapter 3
5
3
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6
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3.
Problem 1 Constructing Parallel Lines
Got It? Reasoning The diagram below shows the construction
of line m through point N with line m parallel to line <. Why must
lines <and m be parallel?
m
N 1
H
J
7. The diagram shows the construction of congruent
angles
and
.
8. Circle the description(s) of the angle pairs that were constructed.
alternate exterior
alternate interior
same-side exterior
corresponding
same-side interior
9. Are the angle pairs congruent or supplementary?
congruent / supplementary
10. Now explain why lines / and m must be parallel.
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Problem 2 Constructing a Special Quadrilateral
*Got) It?
* ) Draw a segment. Label its length m. Construct quadrilateral ABCD with
AB n CD , so that AB 5 m and CD 5 2m.
Underline the correct word or symbol to complete each step.
11. You need to construct parallel / perpendicular lines by constructing congruent
alernate interior / corresponding angles.
* )
* )
* )
12. Draw AB . Draw point D not on AB . Draw AD . The length of
AB / AD is m.
13. At D, construct /TDZ perpendicular / congruent to /DAB so that /TDZ and
* ) * )
/DAB are corresponding angles. Then DZ 6 AB .
* )
14. Now, you need a side of length 2m. Construct C on DZ so that DC 5 2m.
Draw BC / BA .
163
Lesson 3-6, Part 1
15. Do the construction below.
A
m
B
Lesson Check • Do you know HOW?
Draw a line < and a point P not on the line.
Construct the line through P parallel to line <.
16. Line / and point P not on the line are drawn
* )
P
for you. Draw AP .
Complete each statement below and construct
line m.
I
A
17. At P, construct a corresponding angle
congruent to /
B
.
Lesson Check • Do you know HOW?
Look at the diagram. What is the next step in the construction of parallel lines?
19. The steps to construct parallel lines are listed below. Place a ✔
next to each step that is already completed. Place an ✘ next to each
step that has not been completed.
X
O
Y
Draw a line and a point X not on the line.
Label point Y on the line.
* )
Draw XY .
At X, construct a corresponding angle congruent to /Y .
20. What is the next step in the construction of parallel lines?
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Chapter 3
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18. Label the new line m. Line m is parallel to
line / by the 9 Theorem.