Alternate Exterior Angles: Definition & Theorem

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  • 0:00 Definition of…
  • 0:58 The Theorem
  • 1:57 Identifying Alternate…
  • 2:45 Measuring Alternate…
  • 3:32 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, learn why the concept of alternate exterior angles is so important and so very useful for you when you are working with a pair of parallel lines.

Definition of Alternate Exterior Angles

When you have two lines and a third line crossing through them, the pairs of angles that are outside both lines and on alternating sides of the third line are your alternate exterior angles.

Alternate exterior angles.
alternate exterior angles

In the illustration above, angles 1 and 8 make a pair of alternate exterior angles and angles 2 and 7 make another pair of alternate exterior angles. Notice how the pairs are on either side of the line that cuts through the other two lines and all the angles are outside the two lines. The line that cuts through the other two lines is called the transversal. We will use this term from this point going forward.

An easy way to remember these pairs is to think of the words alternate and exterior. The two angles are on alternate or opposite sides of the transversal and the exterior or outside of the two lines. You will always have two pairs of alternate exterior angles when you have two lines and a transversal.

The Theorem

What happens when the two lines are parallel to each other? This is where you get the alternate exterior angles theorem, which states that when you have a pair of parallel lines that are cut by a transversal, the alternate exterior angles are congruent. It is a very useful tool for parallel lines and the angles created by a transversal through those parallel lines. Let's look at it visually again.

Alternate exterior angles when the lines are parallel.
alternate exterior angles

Looking at the illustration above, the two teal-colored lines are parallel to each other. Because these lines are parallel, the theorem tells us that the alternate interior angles are congruent. So, that means that angles 1 and 8 are congruent, or the same, and angles 2 and 7 are congruent as well.

Remember, you will have congruent alternate exterior angles only when the two lines are parallel. If the lines aren't parallel, then you can't say that for sure.

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