sec. 3-3 parallel and perpendicular lines objective: to relate parallel & perpendicular lines
TRANSCRIPT
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