The concept of slope of a line may be taught with an embossed diagram.
- Condition for two lines to be parallel
Let AB and CD be any two parallel lines making angles θ 1 and θ 2 with the positive
direction of the x-axis. Let their slopes be m 1 and m 2 respectively.
Therefore, m 1 = tan θ 1 and m 2 = tan θ2. Since the lines AB and CD are parallel to each
other, θ 1 = θ 2 (corresponding angles)
Therefore, tan θ 1 = tan θ 2
That is m 1 = m 2
Hence if two lines are parallel they have the same slope.
As the idea of “parallel lines” has already been taught the child needs only some
additional input regarding parallel lines in terms of slope of a line.
- Condition for two lines to be perpendicular
If two lines are perpendicular to each other then the product of their slopes equals -1.
That is, if two lines are perpendicular to each other their slopes are negative reciprocals
of each other; conversely, if the slopes of any two lines are negative reciprocals of
each other, the lines are perpendicular.
Y B
D
C
A
X
Y 1
O
θ 1 θ 2
