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High School Geometry: Tutoring Solution14 chapters | 161 lessons

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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.

**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.*

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.

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**

Now, let's pretend that we know that lines *a* and *b* are parallel and angle 3 is 70 degrees. What conclusion could we draw about angle 6 knowing this information? We could conclude that angle 6 is 110 degrees! How can we do this? Because we know that lines *a* and *b* are parallel. Therefore, we know that the same-side interior angles 3 and 6 are supplementary, or that they add up to 180 degrees. Therefore, if angle 3 is 70 degrees, it would make its same-side interior angle, 6, 110 degrees!

**Same-side interior angles** are formed when a **transversal line** intersects two or more lines. When the lines that the transversal intersects are **parallel**, you get same-side interior angles that are **supplementary**, or add up to 180 degrees. If you don't know if the lines in a diagram are parallel, but you know that the same-side interior angles add up to 180 degrees, it's safe to draw the conclusion that the lines cut by the transversal line are parallel and vice versa.

- Same-side interior angles are formed from two parallel lines crossed by a transversal.
- Same-side interior angles add up to 180 degrees.
- To prove two lines are parallel, add up the same-side interior angles, or vice-versa.

Progress through this lesson in order to:

- Identify same-side interior angles
- Use the same-side interior angle theorem to prove parallel lines

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High School Geometry: Tutoring Solution14 chapters | 161 lessons

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