Sec. 3-3Sec. 3-3Parallel and Perpendicular Parallel and Perpendicular

LinesLines

Objective: Objective: To relate Parallel & Perpendicular Lines.To relate Parallel & Perpendicular Lines.

Th(3-9) If two lines are // to the Th(3-9) If two lines are // to the same line, then they are // to same line, then they are // to each other.each other.

kk

mm

nn

11 22

33 44

55 66

77 88

99 1010

1111 1212

tt

Th(3-9) If two lines are // to the Th(3-9) If two lines are // to the same line, then they are // to same line, then they are // to each other.each other.

kk

mm

nn

55 66

77 88

99 1010

1111 1212

tt

Th(3-10) In a plane, if 2 Th(3-10) In a plane, if 2 lines are perpendicular to lines are perpendicular to the same line, then they are the same line, then they are // to each other.// to each other.

rr

ss

tt

Th(3-11) In a plane, if a line Th(3-11) In a plane, if a line is perpendicular to one of is perpendicular to one of two parallel lines, then it is two parallel lines, then it is parallel to the other.parallel to the other.

rr

ss

tt

rr

ss

tt

Corresponding Angles are Corresponding Angles are

They are = 90They are = 90

Alt. Int. Alt. Int. s are s are

They are = 90They are = 90

Same-sided int. Same-sided int. s are Supplementarys are Supplementary

They are both = 90They are both = 90

Example 1: Solve for x and then solve for each angle such that n // m.

14 + 3x

5x - 66

n

m

14 + 3x = 5x -66

-3x -3x

14 = 2x – 66

+66 +66

80 = 2x

2 2

40 = x

14 + 3x

14 + 3(40) =

134

5x – 66

5(40) – 66

134

Example 2: Find the mExample 2: Find the m11

62

7x - 8

7x – 8 + 62 = 180

7x + 54 = 180

7x = 126

x = 18

1

7x – 8

7(18) – 8

118