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 both these cases:

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’ll never meet!

Pairs of Angles

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:


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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, or a = e
Alternate Interior Angles are equal, or c = f
Alternate Exterior Angles are equal, or b = g
Consecutive Interior Angles add up to 180° d + f = 180°
   
... then the lines are Parallel

Examples

These lines are parallel, because a pair of Corresponding Angles are equal.
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