Parallel Lines, and Pairs of Angles

Parallel Lines

Lines are parallel if they are always the same distance apart (called "equidistant"), and 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:

Example 1		Example 2

Parallel lines also point in the same direction.

Try it yourself:

Pairs of Angles

When parallel lines are crossed by another line (called a Transversal), special angle relationships appear.

In this example, many angles are equal and form pairs of angles with unique names.

Click on each name below 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 these special angle pairs can be used to test if lines really are parallel:

If any ... Example: (from diagram) Corresponding Angles are equal a = e or   Alternate Interior Angles are equal c = f or   Alternate Exterior Angles are equal b = g or   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