Parallel Lines, and Pairs of Angles

Parallel Lines

Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Just remember:

Always the same distance apart and never touching.

The red line is parallel to the blue line in each of these examples:

Parallel Example 1 Parallel Example 2
Example 1
Example 2

Parallel lines also point in the same direction.

Parallel lines have so much in common. It's a shame they will never meet!

Try it yourself:


Pairs of Angles

parallel lines angle example

When parallel lines get crossed by another line (which is called a Transversal), you can see that many angles are the same, as in this example:


These angles can be made into pairs of angles which have special names.

Click on each name to see it highlighted:


Now play with it here. Try dragging the points, and choosing different angle types. You can also turn "Parallel" off or on:


Testing for Parallel Lines

Some of those special pairs of angles can be used to test if lines really are parallel:

If Any Pair Of ... Example:
Corresponding Angles are equal a = e
Alternate Interior Angles are equal c = f
Alternate Exterior Angles are equal b = g
Consecutive Interior Angles add up to 180° d + f = 180°
... then the lines are Parallel
parallel angle pairs


These lines are parallel, because a pair of Corresponding Angles are equal. parallel angle example 110 110
not parallel angle 81 101 These lines are not parallel, because a pair of Consecutive Interior Angles do not add up to 180° (81° + 101° =182°)
These lines are parallel, because a pair of Alternate Interior Angles are equal parallel angle example 70 70


813, 814, 1783, 3298, 815, 816, 1784, 1785, 3299, 3300