13.3 parallel and perpendicular lines. parallel lines coplanar lines that do not intersect
TRANSCRIPT
13.3 Parallel and Perpendicular Lines
Parallel Lines
• Coplanar lines that do not intersect
Theorem
• Two nonvertical lines are parallel if and only if their slopes are equal
3
21 m
3
22 m
21 mm
Perpendicular lines
positivem 1negativem 2
Theorem
• Two nonvertical lines are perpendicular if and only if the product of their slopes is -1.
121 mm
In english
• That means that the slopes of two perpendicular lines are– Opposite (one + and one -)– Reciprocals ( and )
3
2
2
3
White Board Practice
• r || s and r t
Slope of r Slope of s Slope of t
2
1
White Board Practice
• r || s and r t
Slope of r Slope of s Slope of t
2
1 22
1
White Board Practice
• r || s and r t
Slope of r Slope of s Slope of t
6
1
White Board Practice
• r || s and r t
Slope of r Slope of s Slope of t
6
16 6
White Board Practice
• r || s and r t
Slope of r Slope of s Slope of t
4
White Board Practice
• r || s and r t
Slope of r Slope of s Slope of t
444
1
Remote Time
The slopes of two lines are given. Are the lines
A: Parallel
B: Perpendicular
C: Neither
D: I don’t know
A: ParallelB: Perpendicular
C: NeitherD: I don’t know
4
3
16
12
A: ParallelB: Perpendicular
C: NeitherD: I don’t know
1 1
A: ParallelB: Perpendicular
C: NeitherD: I don’t know
3 3
A: ParallelB: Perpendicular
C: NeitherD: I don’t know
3 3
A: ParallelB: Perpendicular
C: NeitherD: I don’t know
4
3
3
4
A: ParallelB: Perpendicular
C: NeitherD: I don’t know
33
1
A: ParallelB: Perpendicular
C: NeitherD: I don’t know
3
23
2
A: ParallelB: Perpendicular
C: NeitherD: I don’t know
0 1
A: ParallelB: Perpendicular
C: NeitherD: I don’t know
6
5
5
6
White Board Practice
• Use slopes to show that a quadrilateral with vertices A(-2,7), B(3,7), C(6,11), and D(1,11) is a parallelogram.