Parallel And Perpendicular Lines Worksheet Page 33
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50PROOF
Write a two-column proof for each of the following.
34. Given:
2
1
35. Given: AD
CD
1
3
1
2
Prove: ST UV
Prove: BC
CD
S
V
C
D
1
2
1
W
2
B
3
T
U
A
36. Given: JM KN
37. Given:
RSP
PQR
1
2
QRS and
PQR are
supplementary.
3
4
Prove: KM LN
Prove: PS QR
J
K
L
R
S
1
2
3 4
M
N
Q
P
Determine whether each pair of lines is parallel. Explain why or why not.
38.
39.
y
y
2
( 0, 1.5 )
D
( 4, 4 )
B
( 1.5, 1.8 )
C
1
D
( 4, 1 )
( 4, 2 )
A
O
x
O
x
2
1
1
2
( 0, 0 )
C
( 2,
1.5 )
B
1
( 1,
0.75 )
A
2
40.
HOME IMPROVEMENT
To build a fence, Jim
pickets
positioned the fence posts and then placed a
2 x 4
board
2
4 board at an angle between the fence posts.
As he placed each picket, he measured the angle
that the picket made with the 2
4. Why does
this ensure that the pickets will be parallel?
John Playfair
FOOTBALL
41.
When striping the practice
football field, Mr. Hawkinson first painted the
In 1795, John Playfair
fence posts
published his version
sidelines. Next he marked off 10-yard
of Euclid’s Elements. In
increments on one sideline. He then constructed
his edition, Playfair
lines perpendicular to the sidelines at each
standardized the notation
10-yard mark. Why does this guarantee that
used for points and figures
the 10-yard lines will be parallel?
and introduced algebraic
notation for use in proofs.
42.
CRITICAL THINKING
When Adeel was working
Source:
on an art project, he drew a four-sided figure
with two pairs of opposite parallel sides. He
noticed some patterns relating to the angles in
the figure. List as many patterns as you can about
a 4-sided figure with two pairs of opposite parallel sides.
RESEARCH
43.
Use the Internet or other resource to find mathematicians like
John Playfair who discovered new concepts and proved new theorems related
to parallel lines. Briefly describe their discoveries.
156 Chapter 3 Parallel and Perpendicular Lines
Brown Brothers
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