Name
Class
Date
Practice
3-3
Form K
Proving Lines Parallel
Which lines or segments are parallel? Justify your answer.
1.
2.
r
t
B
D
q
s
A
J
K
L
4.
M
102 68
112
40
E
C
AB n CD; Converse to Corresp. ' Thm.;
BC n DE; Converse to Corresp. ' Thm.
q n s; Converse to Alt. Ext. ' Thm.
3.
40
S
N
Q P
O
PK n MN; Converse to Same-Side Int.
' Post; NM n QJ and JM n QN; Given
T
U
R
XW V
SX n UV ; Converse to Corresp. ' Thm.
5. Developing Proof Complete the flow proof below.
1
Given: /1 and /4 are supplementary.
2
Prove: a 6 b
b
3
4
2 and 3 are
supplementary.
1 and 4 are
supplementary.
Given
1 2 and
3 4
aIb
Substitution
Property
Converse of
Same-Side Int. Post.
Vert. are .
6. Mrs. Jensen made a quilt for her nephew. The
pattern for one block is shown at the right. If
m/1 5 60 and m/2 5 115, are the two gray strips
of fabric parallel? Explain.
No; answers may vary. Sample: l1 and l2 are same-side
int. '. For the strips of fabric to be n, l1 and l2 must
be suppl., but 115 1 60 u 180.
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25
a
1
2
Name
Class
3-3
Date
Practice (continued)
Form K
Proving Lines Parallel
Algebra Find the value of x for which a n b.
7.
8.
65
a
b
(6x 17)
(x 72)
b
43
9.
143
a
21
10.
a
a
(7x 2)
(3x)
(6x)
b
b
(12x)
(8x 14)
16
12
x
Developing Proof Use the given information to
determine which lines, if any, are parallel. Justify
each conclusion with a theorem or postulate.
s
t
1 2
7 8 12
y
3 4
9 10
6 5
11. /8 is supplementary to /9.
x n y; Converse of Same-Side
Int. ' Post.
12. /7 > /4
13. /9 is supplementary to /12.
s n t; Converse of Same-Side
Int. ' Post.
14. /9 > /11
s n t; Converse Of
Alt. Int. ' Thm.
11
x n y; Converse Of
Alt. Ext. ' Thm.
15. Error Analysis A classmate said that AB 6 DC
A
W
based on the diagram at the right. Explain your
classmate’s error. You can’t prove that AB n DC with the
information given because the congruent angles aren’t
formed by the same transversal.
D
Z
Algebra Determine the value of x for which c n d.
Then find ml1 and ml2.
16. m/1 5 100 2 x, m/2 5 40 1 2x
20; 80; 80
1
c
d
17. m/1 5 90 2 6x , m/2 5 100 2 8x
5; 60; 60
2
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26
Y C
X B