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PROOF

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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Parent category: Education