#### Recognizing Alternate and Corresponding Angles

Sometimes it is helpful to hear or read the thought process of others. In this article, you’ll find my thought process on ways to remember the alternate interior, alternate exterior, and corresponding angles. Hopefully, these math tips will help you as they have helped other students.

We begin with the assumption that lines

*a*and

*b*are parallel and another line called a transversal intersects both lines. In the above diagram, the transversal is the red line.

Also, let’s get an understanding of what angles are considered interior and exterior.

**Exterior**- Based upon the diagram above, the exterior represents the angles immediately above line a (<1 and <2) and the angles immediately below line b (<7 and <8).

**Interior**- Based on the diagram above, the interior is referred to those angles located between lines a and line b. (<3, <4, <5, <6)

**III. Alternate interior angles:**

Thought process: Remember, alternate is relative to the transversal.

What are some other words associated with the word alternate? Switch, change, opposite

Look at the interior angles. <3 and <6 are considered alternate interior angles. How can I remember this? Well, first of all, the angles are inside. Then, search for angles that are opposite of each other relative to the transversal and they are diagonal. Another way to make an association is to think I’m looking for two inside angles that alternate sides and are diagonal to one another. Name two other alternate interior angles. Yes, <4 and <5.

**IV. Alternate exterior angles:**

Thought process: These angles are similar to alternate interior angles except that I’m looking for angles that are on the outside. Therefore, the only angles under consideration are <1, <2, <7, and <8. Take a moment and look at the diagram. What pair of outside or exterior angles appears to have alternated or switched positions in a diagonal manner? <1 and <8; <2 and <7.

A student asked the following question: “Why can’t angles <3 and <8 be considered alternate exterior angles?” Can you explain? The two angles are diagonal of each other and <8 is an exterior angle, BUT <3 is an interior angle.

**V. Corresponding angles:**

Four pair of corresponding angles: <1 and <5; <2 and <6; <3 and <7; <4 and <8

Thought process: What do these pairs have in common to help us remember how to identify corresponding angles? Think of the word corresponding as having the same relationship or having the same position relative to the parallel lines and the transversal.

For instance, <1 and < 5 are both on top, as well as <2 and <6. Secondly, notice, each pair of angles is on the same side of the transversal. <1 and <5 are both on the left side of the transversal. Loosely, corresponding angles are angles that are on the same side and whose positions are similar to one another. One position of an angle corresponds to another angle’s position on the same side of the transversal. What other ways can you make a connection?

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