Parallel Lines

What Are Parallel Lines?

• Parallel lines are two lines on a plane that never intersect.

• The symbol for parallel lines is

  . If line AB is parallel to line CD, it would be written as AB

  CD.

Properties of Parallel Lines

• If drawn to scale, parallel lines maintain a constant distance apart from each other.
• Parallel lines are always the same length.
• Parallel lines have the same gradient if they are graphed on a coordinate plane.
• Parallel lines can be horizontal, vertical, or at any angle so long as their gradients match.

Parallel Lines and Angles

• Angles formed by a transversal line cutting through parallel lines have unique properties.
• Alternate angles are equal. These are the angles that are on opposite sides of the transversal, but inside the parallel lines.
• Corresponding angles are also equal. These are the angles in the same relative position at each intersection where a straight line crosses two others.
• Interior consecutive (co-interior) angles on the same side of the transversal add up to 180 degrees (are supplementary). This means they form a straight line.
• Vertically opposite angles are always equal. These are the angles directly across from each other where two lines intersect.

Identifying Parallel Lines

• Parallel lines can be identified through their equal angles. If the alternate, corresponding, or interior angles are equal, the lines are parallel.
• On a graph, parallel lines can be identified by comparing their gradients. If the gradients are equal, the lines are parallel.