Two lines are said to be parallel when:
(a) They are equidistant from each other
(b) Do not intersect or meet
Below are some examples of Parallel Lines
From the above image you can see three set of parallel lines.
Observe how the parallel lines are equidistant to each other at all points and there is no chance that they will intersect each other if extended further.
I hope you get the idea of the concept.
Now let me ask you one question
Tell me if the below lines are parallel or not.
These two lines are not parallel because:
(a) They are not equidistant from each other at all points (observe the green arrows in below image)
(b) If we extend both the lines, they will intersect each other
Constructing Parallel Lines
Here we will discuss two methods for drawing parallel lines.
(a) Using Ruler
(b) Using Protractor
Drawing Parallel lines using Ruler
(a) Take a ruler and draw a straight line using the ruler’s lower side
(b) Now draw straight line using ruler’s upper side.
You can also slide the ruler above or below to get the desired gap between the parallel lines
(c) Remove the ruler and you will get the parallel lines
Drawing Parallel lines using Protractor
(a) Take Protractor and draw straight line using Protractor’s straight side
(b) Draw a 90 degree line M using the protractor
(c) Now Rotate the Protractor and draw 90 degree on line M
(d) After removing the protractor and red line, you will get lines parallel to each other
Angle Properties of Parallel Lines
When the parallel lines are intersected by a transversal then following angle properties are observed:
(01) Corresponding angles are equal
\angle 1\ =\ \angle 5
\angle 2\ =\ \angle 6
\angle 4\ =\ \angle 8
\angle 3\ =\ \angle 7
(02) Alternate Interior angles are equal
\angle 4\ =\ \angle 6
\angle 3\ =\ \angle 5
(03) Alternate Exterior Angles are equal
\angle 1\ =\ \angle 7
\angle 2\ =\ \angle 8
(04) Same Side Interior Angles are Supplementary
\angle 4\ + \ \angle 5 = 180 degree
\angle 3\ + \ \angle 6 = 180 degree
Corollary of Angle Property
I hope you understood the above angle property of parallel line.
Corollary of the property states that if you prove any of the above angle properties, it means that the lines are parallel.
(a) If the pair of corresponding angles are equal, it means that the lines are parallel.
(b) If the alternate angles are equal then it means lines are parallel.
(c) If Same Side Interior Angles are supplementary, it means lines are parallel.
The concept is very simple.
Parallel lines leads to Angle Property.
Angle Property leads to Parallel Lines.
Parallel Line Questions
(01) Test if the lines M & N are parallel or notRead Solution
Observe that \angle A\ & \angle B are corresponding angles.
Also both these angles are equal
\angle A\ =\ \angle B = 75 degree
If corresponding angles are equal, then the line involved are parallel lines.
Hence line M & N are parallel to each other
(02) Check if the below lines are parallel or notRead Solution
The lines are not parallel because if we extend both the lines, they will intersect at certain point
(03) Check if the below lines are parallel or not?Read Solution
From the above image one can observe that angle A & B are Same Side Interior Angle
If the above lines are parallel, then sum of angle A & B will be 180 degree
Angle A + Angle B = 78 + 105
Angle A + Angle B = 183
Hence, the angles are not supplementary.
So the lines are not parallel to each other