### 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.

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

If

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

If then

Suppose you were presented with two angles that are on the same side of a transversal and between the two parallel lines crossed by the transversal. How would you describe these angles and what could you conclude about their measures?

### Examples

#### Example 1

Is

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

#### Example 2

Give two examples of same side interior angles in the diagram:

There are MANY examples of same side interior angles in the diagram. Two are

#### Example 3

Find the value of

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

#### Example 4

Find the value of

#### Example 5

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 parallel? Justify your answer.

In 4-5, use the given information 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 6-8, 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)∘

For 9-10, 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.

### Review (Answers)

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