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Name ________________________________________ Date __________________ Class__________________
LESSON
3-1
Reteach
Lines and Angles
Lines
Description
Examples
parallel
lines that lie in the same plane
and do not intersect
symbol: ||
perpendicular
lines that form 90° angles
symbol: ⊥
skew
lines that do not lie in the
same plane and do not
intersect
A || m
k and m
are skew.
k⊥ A
Parallel planes are planes that do not intersect. For example, the top and bottom of
a cube represent parallel planes.
Use the figure for Exercises 1–3. Identify each of the following.
1. a pair of parallel lines
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2. a pair of skew lines
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3. a pair of perpendicular lines
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Use the figure f or Exercises 4–9.
Identify each of the following.
5. a segment that is perpendicular to GH
4. a segment that is parallel to DG
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6. a segment that is skew to JF
7. one pair of parallel planes
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8. one pair of perpendicular segments,
not including GH
9. one pair of skew segments,
not including JF
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3-6
Holt McDougal Geometry
Name ________________________________________ Date __________________ Class__________________
LESSON
3-1
Reteach
Lines and Angles continued
A transversal is a line that intersects two lines in a plane
at different points. Eight angles are formed. Line t is a
transversal of lines a and b.
Angle Pairs Formed by a Transversal
Angles
Description
Examples
corresponding
angles that lie on the same side of
the transversal and on the same
sides of the other two lines
alternate interior
angles that lie on opposite sides of
the transversal, between the other
two lines
alternate exterior
angles that lie on opposite sides of
the transversal, outside the other two
lines
same-side interior
angles that lie on the same side of
the transversal, between the other
two lines; also called consecutive
interior angles
Use the figure for Exercises 10–13.
Give an example of each type of
angle pair.
10. corresponding angles
11. alternate exterior angles
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12. same-side interior angles
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13. alternate interior angles
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Use the figure for Exercises 14–16.
Identify the transversal and classify
each angle pair.
14. ∠1 and ∠2
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15. ∠2 and ∠4
16. ∠3 and ∠4
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
3-7
Holt McDougal Geometry
Answers for the chapter Parallel and Perpendicular Lines
Practice C
3-1 LINES AND ANGLES
1.
Practice A
1. Skew
2. intersect
3. 90° or right
4. Parallel
5. AC & EG
Lines j and A are parallel.
6. AC and Dh are skew.
2.
7. CG ⊥ EG
8. plane ABD || plane EFH
9. lines
10. Corresponding
11. outside
12. Alternate
13 same
14. line r
Lines j and A are skew.
3.
15. ∠1 and ∠3 or ∠2 and ∠4
16. ∠2 and ∠3
17. ∠1 and ∠4
Practice B
Lines j and A are perpendicular.
1. BE & AD
4.
2. AB and CF are skew.
3. CF ⊥ EF
4. plane ABC || plane DEF
5. line z
Lines j and A are parallel.
6. lines x and y
7. Sample answer: ∠1 and ∠3
5. X = 10; O = 10
8. Sample answer: ∠2 and ∠6
6. X = 40; O = 70
7.
9. Sample answer: ∠1 and ∠5
10. Sample answer: ∠2 and ∠3
11. transv.: utility pole; same-side interior
angles
8.
12. transv.: tension wire; alternate exterior
angles
13. transv.: telephone line; corresponding
angles
14. transv.: utility pole; alternate interior
angles
Reteach
1. g || h
2. j and h
3. j ⊥ g
4. Possible answers: EH or FJ
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Holt McDougal Geometry
3. All four segments are marked with the
same arrows.
4. Sample answer: Parallel lines are
coplanar lines that never intersect, and
perpendicular lines intersect at 90° angles.
5. Sample answer: HJ
6. Sample answer: DE
7. plane DEF || plane GHJ
8. Sample answer: DE ⊥ EF
9. Sample answer: HE and DF
10. Sample answer: ∠1 and ∠3
11. Sample answer: ∠1 and ∠8
12. Sample answer: ∠2 and ∠3
13. Sample answer: ∠2 and ∠7
14.transv. n; same-side int. ∠s
15. transv. m; alt. ext. ∠s
16. transv. p; corr. ∠s
3-2 ANGLES FORMED BY PARALLEL
LINES AND TRANSVERSALS
Practice A
2. no; yes
3. PR + RQ = PQ
4. The distance PR + RQ, the length of the
path from P to Q traveling in a
counterclockwise direction, is much
longer than the length of the path
traveling from P to Q in a clockwise
direction. So, PR + RQ ≠ PQ.
5. Any two lines will intersect at exactly two
points.
6. If the two points are at opposite “poles,”
then infinitely many lines will pass
through them.
Problem Solving
1. Sample answer: No; AP is skew to RS
and RS is skew to AD , but AP is not
skew to AD .
3.
4.
5.
7.
5. 75
6. 150
9. congruent
11. ∠1 and ∠7; ∠2 and ∠8
12. ∠3 and ∠6; ∠4 and ∠5
Practice B
1. 47°
3. 97°
2. 119°
4. 62°
5.
Statements
Reasons
1. p �� q
1. Given
2. a. m∠2 + m∠3 = 180°
2. Lin. Pair Thm.
3. ∠1 ≅ ∠2
3. b. Corr. ∠s Post.
4. c. m∠1 = m∠2
4. Def. of ≅ ∠s
5. d. m∠1 + m∠3 = 180°
5. e. Subst.
6. 15; 40
Practice C
1. Sample answer: m∠1 + m∠2 = 180° and
m∠3 + m∠4 = 180° by the Same-Side Int.
∠s Thm. Thus, the total of the angle
measures is 360°.
2. 360°
Reading Strategies
2. Yes, there is a right angle box at their
intersection.
4. 70°
10. ∠3 and ∠5; ∠4 and ∠6
CF
Sample answer: ∠DEB and ∠CBE
B parallel lines
6. J skew
A
1. LP and MQ
3. 140°
8. supplementary
2. Sample answer: No; PQ is skew to AD
but not to PS .
2. equal
7. parallel; transversal
Challenge
1. no; no
1. congruent
3. 360°; sample answer:
Statements
Reasons
HJJG
1. Draw BE parallel to AD.
1. Construction
2. m∠1 + m∠ABE = 180°,
m∠4 + m∠DEB = 180°
2. Same-Side Int.
∠s Thm.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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Holt McDougal Geometry