Download 3.2 practice

Name ________________________________________ Date __________________ Class__________________
LESSON
3-2
Practice B
Angles Formed by Parallel Lines and Transversals
Find each angle measure.
1. m∠1 _______________________
2. m∠2 _______________________
–
+
3. m∠ABC _______________________
4. m∠DEF _______________________
Complete the two-column proof to show that same-side exterior angles
are supplementary.
1
5. Given: p || q
Prove: m∠1 + m∠3 = 180°
p
2
q
3
Proof:
Statements
Reasons
1. p || q
1. Given
2. a. _______________________
2. Lin. Pair Thm.
3. ∠1 ≅ ∠2
3. b. _______________________
4. c. _______________________
4. Def. of ≅ ∠s
5. d. _______________________
5. e. _______________________
6. Ocean waves move in parallel lines toward the shore.
The figure shows Sandy Beaches windsurfing across
several waves. For this exercise, think of Sandy’s wake
as a line. m∠1 = (2x + 2y)° and m∠2 = (2x + y)°.
Find x and y.
x = _________
y = _________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
3-12
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.
A22
Holt McDougal Geometry