What if you were presented with two angles that are on the same side of a transversal, but inside the lines? How would you describe these angles and what could you conclude about their measures?

### Same Side Interior Angles

**Same Side Interior Angles** are two angles that are on the same side of the transversal and on the interior of (between) the two lines. and

**are same side interior angles.**

∠5

**Same Side Interior Angles Theorem:** If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.

So, if

**Converse of the Same Side Interior Angles Theorem:** If two lines are cut by a transversal and the consecutive interior angles are supplementary, then the lines are parallel.

#### Recognizing Same Side Interior Angles

Using the picture above, list all the pairs of same side interior angles.

Same Side Interior Angles:

#### Measuring Angles

1. Find

Here,

This example shows why if two parallel lines are cut by a transversal, the same side interior angles are supplementary.

2. Find the measure of

The given angles are same side interior angles. The lines are parallel, therefore the angles add up to

### Examples

#### Example 1

Is

These are Same Side Interior Angles. So, if they add up to

#### Example 2

Find the value of

The given angles are same side interior angles. Because the lines are parallel, the angles add up to

#### Example 3

Find the value of

These are same side interior angles so set up an equation and solve for

### Review

For questions 1-2, use the diagram to determine if each angle pair is congruent, supplementary or neither.

∠5 and∠8 ∠2 and∠3 - Are the lines in the diagram parallel? Justify your answer.

In 4-5, use the given diagram to determine which lines are parallel. If there are none, write none. Consider each question individually.

∠AFD *and*∠BDF are supplementary∠DIJ *and*∠FJI are supplementary

For 6-11, what does the value of

m∠3=(3x+25)∘ andm∠5=(4x−55)∘ m∠4=(2x+15)∘ andm∠6=(3x−5)∘ m∠3=(x+17)∘ andm∠5=(3x−5)∘ m∠4=(3x+12)∘ andm∠6=(4x−1)∘ m∠3=(2x+14)∘ and \begin{align*}m\angle 5 = (3x-2)^\circ\end{align*}- \begin{align*}m\angle 4 = (5x+16)^\circ\end{align*} and \begin{align*}m\angle 6 = (7x-4)^\circ\end{align*}

For 12-13, determine whether the statement is true or false.

- Same side interior angles are on the same side of the transversal.
- Same side interior angles are congruent when lines are parallel.

For questions 14-15, use the image.

- What is the same side interior angle with \begin{align*}\angle 3\end{align*}?
- Are the lines parallel? Explain.

### Review (Answers)

To view the Review answers, open this PDF file and look for section 3.6.