Constructing Parallel
and Perpendicular Lines
3-6
Vocabulary
Review
Write T for true or F for false.
1. A rectangle has two pairs of parallel segments.
2. A rectangle has two pairs of perpendicular segments.
Write alternate exterior, alternate interior, or corresponding to describe each
angle pair.
4.
1
2
5.
4
5
3
6
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
78
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3.
Problem 1 Constructing Parallel Lines
Got It? Reasoning The diagram at the right 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
7. The diagram shows the construction of congruent
angles
and
H
.
J
8. Circle the description(s) of the angle pairs that were constructed.
alternate interior
congruent
corresponding
same-side interior
9. 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 sentence.
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10. Construct parallel / perpendicular lines.
* )
* )
* )
11. Draw AB . Draw point D not on AB . Draw AD . The length of
AB / AD is m.
12. At D, construct /TDZ perpendicular / congruent to /DAB so that /TDZ and
* ) * )
/DAB are corresponding angles. Then DZ 6 AB .
* )
13. Now, you need a side of length 2m. Construct C on DZ so that DC 5 2m.
Draw BC / BA .
14. Do the construction below.
A
m
B
79
Lesson 3-6
Problem 3
Perpendicular at a Point on a Line
* )
* )
* )
* )
Got It? Use a straightedge to draw EF . Construct FG so that FG ' EF at point F.
15. Use the diagram at the right. Write each construction step.
G
Step 1
_________________________________________
E
F
H
Step 2
_________________________________________
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Step 3
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Step 4
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Step 5
Postulate 3-4 Perpendicular Postulate
Complete the statement of Postulate 3-4 below.
16. Through a point not on a line, there is one and only one line parallel / perpendicular
to the given line.
17. Circle the diagram that models Postulate 3-4.
P
Chapter 3
P
P
80
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Problem 4 Perpendicular From a Point to a Line
* )
* )
* )
* )
* )
Got It? Draw a line CX and a point Z not on CX . Construct ZB so that ZB ' CX .
Underline the correct word(s) to complete each sentence.
18. Open your compass to a size equal to / greater than the distance from Z to line /.
19. With the compass tip on point Z, draw an arc that intersects line / at one / two point(s).
20. Label the point(s) C and X / Z .
21. Place the compass point on C / Z
and make an arc below line /.
Z
22. With the same opening and the
compass tip on C / X , draw an
arc that intersects the arc you
made in Exercise 21. Label the
point of intersection B.
E
* ) * )
23. Draw ZB / CX .
24. Use line / and point Z at the right.
Construct a line through point Z
perpendicular to line /.
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Lesson Check • Do you UNDERSTAND?
Suppose you use a wider compass setting in Exercise 18. Will you construct a different
perpendicular line? Explain.
25. Explain why you will NOT construct a different perpendicular line.
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Math Success
Check off the vocabulary words that you understand.
construction
parallel
perpendicular
Rate how well you can construct parallel and perpendicular lines.
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review
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Now I
get it!
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Lesson 3-6