Study guide

Name———————————————————————— Lesson
3.3
Date —————————————
Study Guide
For use with the lesson “Prove Lines are Parallel”
goal
Use angle relationships to prove that lines are parallel.
Vocabulary
A proof can be written in paragraph form, called a paragraph proof.
Postulate 16 Corresponding Angles Converse: If two lines are cut by
a transversal so the corresponding angles are congruent, then the lines
are parallel.
Theorem 4 Alternate Interior Angles Converse: If two lines are cut
by a transversal so the alternate interior angles are congruent, then the
lines are parallel.
Theorem 5 Alternate Exterior Angles Converse: If two lines are cut
by a transversal so the alternate exterior angles are congruent, then the
lines are parallel.
Theorem 6 Consecutive Interior Angles Converse: If two lines
are cut by a transversal so the consecutive interior angles are
supplementary, then the lines are parallel.
example 1
Apply the Corresponding Angles Converse
Find the value of x that makes j i k.
j
k
Solution
Lines j and k are parallel if the
marked corresponding angles
are congruent.
538
(7x 1 4)8
(7x 1 4)8 5 538
Use Postulate 16 to write an equation.
7x 5 49
Subtract 4 from each side.
x 5 7
Divide each side by 7.
The lines j and k are parallel when x 5 7.
Lesson 3.3
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Theorem 7 Transitive Property of Parallel Lines: If two lines are
parallel to the same line, then they are parallel to each other.
Exercises for Example 1
1. Find the value of x that makes l i m.
1108
(6x 1 2)8
m
Geometry
Chapter Resource Book
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3-39
4/27/11 2:47:44 AM
Name———————————————————————— Lesson
3.3
Date —————————————
Study Guide continued
For use with the lesson “Prove Lines are Parallel”
g
2. Is there enough information in the diagram to h
conclude that g i h? Explain.
708
1108
example 2
Show lines are parallel
Use the diagram at the right.
a. Find the value of x that makes a i b.
b. Find the value of y that makes a i c.
628
a
(5x 2 2)8
b
(7y 1 6)8
c
Solution
a. Lines a and b are parallel if the marked consecutive
interior angles are supplementary.
(5x 2 2)8 1 628 5 1808
Use Theorem 6 to write an equation.
5x 1 60 5 180
5x 5 120
x 5 24
Combine like terms.
Subtract 60 from each side.
Divide each side by 5.
The lines a and b are parallel when x 5 24.
b. Lines a and c are parallel if the marked alternate interior angles
are congruent.
(7y 1 6)8 5 628
Use Theorem 4 to write an equation.
7y 5 56
y 5 8
Subtract 6 from each side.
Divide each side by 7.
The lines a and c are parallel when y 5 8.
Lesson 3.3
Exercises for Example 2
3-40
Find the value of x that makes p i q.
3.
1408
4.
p
q
p
728
(13x 2 3)8
q
(9x)8
5.
988
p
(7x 2 2)8
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
q
Geometry
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CS10_CC_G_MECR710761_C3L03SG.indd 40
4/27/11 2:47:44 AM
c ongruent, alternate interior angles are congruent,
and alternate exterior angles are congruent.
5. If two lines are parallel to the same line, then
they are parallel to each other.
Practice Level A
1. yes; Corresponding Angles Converse
13. p i q 14. neither 15. Given; Alternate
Exterior Angles Theorem; Definition of Congruent
Angles; Given; Definition of Congruent Angles;
Alternate Interior Angles Converse 16. Given;
Alternate Interior Angles Theorem; Definition of
Congruent Angles; Given; Substitution; Definition
of Supplementary Angles; Consecutive Interior
Angles Converse
2. yes; Alternate Interior Angles Converse
Study Guide
3. yes; Alternate Exterior Angles Converse
1. 18 2. Yes; the angle that corresponds with
708 has a measure of 708 because it is a linear pair
with the angle that measures 1108.
3. 11 4. 8 5. 12
4. yes; Corresponding Angles Converse
5. no 6. yes; Alternate Interior Angles Converse
7. 40 8. 30 9. 30 10. 14 11. 32 12. 95
13. C 14. m i n 15. p i q 16. p i q
17. neither 18. Given; Corresponding Angles
Postulate; Given; Transitive Property of
Congruence; Corresponding Angles Converse
19. Each lane is parallel to the one next to it,
so l1 i l2, l2 i l3, and l3 i l4. Then l1 i l3 by
the Transitive Property of Parallel Lines. By
continuing this reasoning, l1 i l4. So, the first
lane is parallel to the last lane.
Practice Level B
1. yes; Consecutive Interior Angles Converse
2. yes; Alternate Interior Angles Converse
3. no 4. 40 5. 109 6.115 7. 22 8. 5 9. 80
10. congruent 11. supplementary 12. congruent
13. Each row is parallel to the one next to it,
so r1 i r2, r2 i r3, and so on. Then r1 i r3 by
the Transitive Property of Parallel Lines.
By continuing this reasoning, r1 i r5. So, the first
row is parallel to the last row. 14. Given
15. Corresponding Angles Postulate 16. Given
17. Transitive Property of Congruence 18. Alternate Exterior Angles Converse 19. Given
20. Alternate Interior Angles Theorem
21. Given 22. Transitive Property of Congruence
23. Alternate Interior Angles Converse
24. Corresponding Angles Converse
Practice Level C
1. no 2. no 3. yes; Alternate Exterior Angles
Converse 4. 16 5. 15 6. 24 7. 45 8. 23
A36
9. 42 10. m i n 11. neither 12. neither
Geometry
Chapter Resource Book
Problem Solving Workshop:
Mixed Problem Solving
@##$ , @BF 
##$ 
1. a. Sample answer: CG
@##$ c. Plane DCG
b. Sample answer: CG
2. Yes. Since line m intersects line j, the angle
formed that is 498 and the one below it are
supplementary. So, the angle below it is 1318. Since
line n intersects line j, the angle formed that is 1318
and the one above it are supplementary. So, the
angle above it is 498. Since a pair of corresponding
angles are congruent, the lines m and n are parallel.
3. 1108 4. Sketches will vary. There are 6 sides
that could be a transversal for a pair of opposite
sides. 5. a. no b. yes c. Line l on any step is
always parallel to line l on any other step because
the line is always going across the width of the
escalator. Plane A on any step is not always parallel
to plane A on any other step. Plane A on the step
that is rising up the escalator is not parallel to
plane A on the step coming down underneath it.
d. 2; When each step is going from facing upward
to facing downward and when each step is going
from facing downward to facing upward
Challenge Practice
1. a. ∠ VXW 5 (180 2 x)8
b. ∠ WXZ 5 (180 2 y)8
c. ∠ VXZ 5 (360 2 x 2 y)8
2. p i q by the Corresponding Angles Converse;
q i r by the Consecutive Interior Angles Converse;
p i r by the Transitive Property of Parallel Lines;
s i t by the Alternate Exterior Angles Converse
3. x 5 6, y 5 9
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answers
Lesson 3.3 Prove Lines are
Parallel, continued

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