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A N S W E RClass
S
Name
Date
page 29
3-1
page 30
Additional Problems
Additional Problems
3-2
Lines and Angles
Problem 1
Properties of Parallel Lines
Problem 1
a. Which segments are parallel to RU ?
Y
b. Which segments are skew to SW ?
V
c. What are two pairs of parallel planes?
R
Which angles measure 130?
X
W
l2, l4, l5
U
1
5
2
T
S
3
6
130
4 8
d. What are two segments parallel to plane RUYV?
a. ST , VY , WX b. RU, VY , XY , TU c. planes RUYV and STXW,
planes RSWV and UTXY planes RUTS and VYXW d. ST , TX ,
SW , WX
Problem 2
Which is a pair of alternate interior angles? B
5
A. /1 and /2
B. /3 and /6
1
7 8
6
3 4
2
Problem 2
C. /2 and /7
Given: a 6 b
D. /4 and /8
Prove: /1 and /3 are supplementary.
1
a
3
b
2
It is given that a n b. So, l1 is congruent to l2 because they
are alternate exterior angles. l3 and l2 are supplementary
because they form a linear pair. So, l1 and l3 are
supplementary by the Congruent Supplements Theorem.
Problem 3
In the figure above, are /3 and /7 alternate interior angles,
same-side interior angles, corresponding angles, or alternate
exterior angles?
corresponding angles
page 31
3-2
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page 32
Additional Problems (continued)
Additional Problems
3-3
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Properties of Parallel Lines
Problem 3
4/23/09 11:40:21 AM
Proving Lines Parallel
Problem 1
What are the measures of /8 and /4?
Explain.
ml8 5 65 because a n b and same
side interior angles of parallel lines
are supplementary angles. ml4 5 115
because m n n and corresponding angles
of parallel lines are equal.
5
2 6
4
3
m
1
8
115
Which lines are parallel if /2 > /3? Justify
your answer.
a
m and n by the Converse of the Alt. Int.
Angles Thm.
b
a
b
1
2 8
3
4
n
5
6
7
m
n
Problem 4
Problem 2
What is the value of y? 70
Use the diagram below. Write a flow proof.
y
60 50
1
2
a
5
4
b
Given: m/5 5 40; m/2 5 140
Prove: a 6 b
m5 40
5 and 2 are supp. .
Given
Definition of supp. a Ib
m2 140
5 and 2 are same-side int. .
Given
Definition of same-side int. Converse of Same-Side Int.
Theorem
Prentice Hall Geometry • Additional Problems
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
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A N S W E RClass
S
Name
Date
page 33
3-3
page 34
Additional Problems (continued)
3-4
Proving Lines Parallel
Problem 3
Additional Problems
Parallel and Perpendicular Lines
Problem 1
If m/1 5 65 and m/2 5 115, are lines
a and b parallel? Explain.
1
Yes, they are same-side interior angles and
are suppl., so lines a and b are parallel.
2
a
What is the relationship between segments
AB and CD? Explain.
b
They are parallel, because they are both
perpendicular to BC .
B
68
22
35
55
C
D
A
Problem 4
Problem 2
What is the value of x for which a 6 b? 43
In a plane, c ' b, b ' d, and d ' a.
Prove that c 6 d.
a
48
(3x 3)
Because c ' b, the lines form right angles.
Also, because b ' d, those lines form
right angles. So, there are corresponding
congruent angles where c intersects b and
where d intersects b. Therefore, c n d by
Theorem 3-8.
b
page 35
3-5
0032_hsm11gmap_0303.indd 33
c
d
a
b
page 36
Additional Problems
3-5
0034_hsm11gmap_0304.indd
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Parallel Lines and Triangles
Problem 1
Additional Problems (continued)
4/23/09 11:37:05 AM
Parallel Lines and Triangles
Problem 2
b. What is the measure of /2? 66
Solve for x, y, and z in the figure below.
2
36 ° 32 °
53 °
z°
y° x°
119 °
46 °
x 5 102, y 5 78, z 5 66
Problem 2
Problem 3
a. What is the measure of /1? 87
What is the value of x? D
1
x°
A. 170
46 °
B. 110
41 °
C. 70
110 °
60 °
D. 50
Prentice Hall Geometry • Additional Problems
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
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