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 1Parallel 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 equala = e
or 
Alternate Interior Angles are equalc = f
or 
Alternate Exterior Angles are equalb = g
or 
Consecutive Interior Angles add up to 180°d + f = 180°
  
... then the lines are Parallel
parallel angle pairs

Examples

These lines are parallel, because a pair of Corresponding Angles are equal.parallel angle example 110 110
not parallel angle 81 101These 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 equalparallel angle example 70 70