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Same-Side Interior Angles: Definition & Theorem

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  • 0:00 What Are Same-Side…
  • 0:40 Same-Side Interior…
  • 1:32 Examples
  • 2:45 Lesson Summary
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Lesson Transcript
Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, you will learn the definition of same-side interior angles, their properties when they lie on parallel lines, and the same-side interior angle theorem. At the end, you can test your knowledge with a quiz.

What Are Same-Side Interior Angles?

Same-side interior angles are a pair of angles on one side of a transversal line, and on the inside of the two lines being intersected. What is a transversal line, you may wonder? A transversal line is simply a line that intersects other lines. This may sound confusing, but this diagram should clear up any uncertainties.

Angles 3 and 6, indicated in pink, are same-side interior angles. Angles 4 and 5, indicated in green, are also same-side interior angles. And line t is the transversal line intersecting lines a and b.

Same-Side Interior Angle Theorem

If you look at the diagram, you might notice something else interesting. Lines a and b are parallel to each other! What are parallel lines? They are lines that run alongside each other that never intersect.

When transversal line t intersects parallel lines a and b, it makes the same-side interior angles 3 and 6 supplementary. Same-side interior angles 4 and 5 are also supplementary. Supplementary angles are angles that add up to 180 degrees.

Surprisingly, we have just covered the same-side interior angle theorem without even knowing it! The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary, or add up to 180 degrees.

Examples

Let us look at two examples before ending this lesson. We will use to the same diagram in both examples.

Example 1

Let's pretend that we don't know if lines a and b are parallel. Let's pretend that we know that angle 4 is 100 degrees and angle 5 is 80 degrees. What conclusion can we draw about lines a and b now? That they are parallel! How do we know this? Because we know that same-side interior angles 4 and 5 equal 180 degrees. Therefore, we can draw the conclusion that lines a and b are parallel!

Example 2

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