Parallel Lines

A unit in almost every geometry class has parallel lines cut by a transversal.

These three lines create a slew of angles that you will need to know and understand. They include corresponding, alternate interior, alternate exterior, same-side interior and same-side exterior.

GradeA will make it easy for your to learn these vocabulary terms, and also how to solve problems using them!

Here's our first tip:


Same-side angles are supplementary (notice the s.s.s.), and the other angles are congruent. We will have a lot more to say about this, as well as some GradeA diagrams to make your life easier!

What are Parallel Lines Anyway?

Two lines that are in the same plane that do not intersect are said to be parallel. (More information about the undefined terms in geometry).

parallel lines

What is a Transversal?

A transversal is a line that intersects two or more lines. When this happens, eight different angles are created, many of which come in special pairs. This becomes particularly interesting whenever the two lines are also parallel because the angles are either congruent or supplementary.

  parallel lines and transversal  

"Interior" vs. "Exterior" Angles - What's the Difference?

Interior: Between the Parallel Lines
Exterior: Outside the Parallel Lines
interior angles
exterior angles

Special Angle Pairs

Corresponding Angles: There are four pairs of corresponding angles that are created by the transversal. The pairs are in the same location in their respective cluster of four. For example, the "top-left" angle corresponds with the other "top-left" angle. See the diagram below.

Top-Left with Top-Left
Top-Right with Top-Right
corresponding angles top left
corresponding angles top right
Bottom-Left with Bottom-Left
Bottom-Right with Bottom-Right
corresponding angles bottom left
corresponding angles bottom right

Alternate Interior Angles: We already know that interior angles are between the two lines. The word alternate means that the angles are on opposite sides of the transveral. See for yourself.

alternate interior angles
alternate interior angles 2

Alternate Exterior Angles: Almost the same as alternate interior, except now the angles are on the outside. See below.

alternate exterior angles
alternate exterior angles 2

Same-Side Interior Angles: Interior angles that are both on the same side of the transversal. See below.

same-side interior angles
same-side interior angles 2

Same-Side Exterior Angles: Exterior angles that are both on the same side of the transversal. See below.

same-side exterior angles
same-side exterior angles

Degree Measures of Special Angle Pairs


Corresponding and alternate angles are congruent. Remember, congruent means they have the same degree measure (it's the geometry equivalent of equals)

Same-side angles are supplementary (remember, sss).

Take a look back at the diagrams above. You should be able to see visually which angles are supplemenatry and which angles are congruent.

Additional Information

Return from parallel lines to other free geometry help topics.

You may also want to visit the GradeA homepage for more free math help resources!    

GradeA also offers a geometry glossary so that you can learn all geometry vocabulary that you will encounter along the way!


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