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CAHSEE Math Exam: Tutoring Solution21 chapters | 211 lessons

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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.

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**.

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.

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.

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.

One type of problem that you will encounter when it comes to the subject of alternate exterior angles is to identify them. You will be given an illustration of two lines and a transversal and you will be asked whether so-and-so angle is an alternate exterior angle. Or you might be asked to find the pairs of alternate exterior angles. For example, you might be asked, is angle 6 an alternate exterior angle to angle 1 and they will give you a picture similar to this. This is the way you word things when you want to say two angles are a pair of alternate exterior angles.

You will look at the picture and ask yourself *is the angle outside the two lines?* and *is it on the opposite side of the transversal as the other angle?* If the answer is no to any of these, then the angle is not. In this example, angle 6 is not an alternate exterior angle to angle 1.

Another type of problem that you will encounter is when you are asked about the measurements of a certain angle given the measurement of its alternate exterior angle. This involves using the theorem and recognizing which angles are congruent to which. For example, you might be asked to find the measurement of angle 1 if the measurement of angle 8 is 120 degrees. You will get a picture similar to this.

You will look at the picture and ask yourself if angles 1 and 8 are alternate exterior angles. If they are, then you know that they are equal to each other. So, if angle 8 is 120 degrees, then so is angle 1. In this case, angles 1 and 8 are alternate exterior angles and therefore angle 1 is also 120 degrees.

**Alternate exterior angles** are angles that are on opposite sides of the transversal and outside the two lines. If the two lines are parallel, then the theorem tells you that the alternate exterior angles are congruent to each other. The two types of problems you will encounter are identifying and measuring problems.

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CAHSEE Math Exam: Tutoring Solution21 chapters | 211 lessons

- The Pythagorean Theorem: Practice and Application 7:33
- How to Identify Similar Triangles 7:23
- Applications of Similar Triangles 6:23
- Classifying Triangles by Angles and Sides 5:44
- Angles and Triangles: Practice Problems 7:43
- Triangle Congruence Postulates: SAS, ASA & SSS 6:15
- Congruency of Isosceles Triangles: Proving the Theorem 4:51
- Congruency of Right Triangles: Definition of LA and LL Theorems 7:00
- Alternate Exterior Angles: Definition & Theorem 4:03
- Pentagonal Prism: Definition & Properties 2:37
- Go to CAHSEE - Triangles, the Pythagorean Theorem & Congruency: Tutoring Solution

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