Applications of Math 10
Name:___________________________
PARALLEL AND PERPENDICULAR LINES ASSIGNMENT
The following pairs of lines are parallel.
C
1. a. Find the slope of AB.
A
8
6
Slope =
rise
= __________
run
4
-8
H
-4
D
4
rise
= __________
run
8
-2
G
c. What do you notice about the
-4
-6
slope of the lines?
_________________________
B
2
b. Find the slope of CD.
Slope=
F
-8
E
-10
2. a. Find the slope of EF.
Slope=
b. Find the slope of GH.
rise
=__________
run
Slope =
rise
= __________
run
c. What do you notice about the slope of the lines?
__________________________________________________________________
3. What can you say about the slopes of parallel lines?
The slope of parallel lines are _______________.
The following pairs of lines are perpendicular.
8
A
1. a. Find the slope of AB.
6
4
Slope
rise
= __________
run
b. Find the slope of CD.
E
2
C
-8
D
G
H
-4
4
8
-2
Slope
rise
= __________
run
c. Multiply the slope of AB by
the slope of CD.
What do you get?
F
-4
-6
B
-8
-10
__________________________________________________________________
2. a. Find the slope of EF.
Slope
rise
= __________
run
b. Find the slope of GH.
Slope
rise
= __________
run
c. Multiply the slope of EG by the slope of GH. What do you get?
__________________________________________________________________
3. What can you say about multiplying the slopes of perpendicular lines?
__________________________________________________________________
Applications of Math 10
Name:___________________________
PARALLEL AND PERPENDICULAR LINES NOTES
Parallel lines - slopes of the lines are ________________
Example:
Line AB Slope =
4
7
Line CD Slope =
4
7
**Lines are parallel because slopes are _________________**
Perpendicular lines - slopes are negative reciprocals of each other
(negative reciprocal - change the sign of the slope and invert it)
Example:
Line AB Slope =
2
3
Line CD Slope = 
3
2
**Slopes are perpendicular because slopes are _____________ _____________**
Important: to make negative reciprocals you change the sign in front
of the number and invert it (flip it upside down)
Example: What is the negative reciprocal of the following numbers?
a.
1
_______
2
b.
5
________
4
c. 
e. 4 ________ f. -5 ________ g.
3
_______
8
d.
13
________
15
8
________
9
h. -10 ________
PRACTICE: Complete the following, showing all your work.
1. The slopes of several line segments are given below.
slope of AB = 2
slope of XY = 
slope of JK =
1
2
slope of GH =
a) Which line segments are parallel?
1
2
1
2
slope of MN = -2
slope of CD = -0.5
b) Which line segments are perpendicular?
2. Complete the following chart if:

Line segment 'a' is parallel to line segment 'b' and,

Line segment ‘a’ is perpendicular to line segment 'c'.
Slope of 'a'
Slope of 'b'
Slope of 'c'
2
5
1

7
-8
11
4

5
9
10
0
3. Two line segments that appear to be parallel are shown below. Calculate the slopes of the line
segments and determine if they are parallel.
16
12
8
4
-16 -12 -8
-4
4
8
12
16
20
-4
-8
-12
-16
-20
4. Two line segments that appear to be perpendicular are shown below. Calculate the slopes of the line
segments and determine if they are perpendicular.
16
12
8
4
-16 -12 -8
-4
4
-4
-8
-12
8
12
16
20
Applications of Math 10
Name:___________________________
5. Determine the slope of each line segment with endpoints given below. Identify which line segments
are parallel and which are perpendicular.
i)
A(5, 3), B(0, 0)
iv)
G(-4, 3), H(-1, -2)
Slope___________
ii)
C(6, -1), D(1, 2)
Slope___________
v)
J(2, 7), K(-1, 5)
Slope___________
iii)
E(-5, -8), F(-2, -6)
Slope___________
Slope___________
6. Determine the value of the variable that satisfies each condition.
a) The slopes of parallel line segments are 3/5 and k/10.
b) The slopes of perpendicular line segments are 1/3 and m/2.
7. To help her map out an arrangement for a flowerbed for her front yard, Verna used a coordinate
grid. The corners of the flowerbed were represented by the coordinates A(0, 8), B(4, 9), C(6, 1),
and D(2, 0). a) Plot the points on a coordinate grid and connect them with line segments.
8
b) Calculate the slopes of all four line segments.
6
_____________
_____________
______________
_____________
4
2
c) What shape is Verna’s flowerbed?
______________________
-8
-6
-4
-2
2
-2
-4
Complete P.236 #1-3, (2 bonus marks) -> #4
-6
-8
-10
4
6
8
10