# UNIT 4 LESSON 1: TRIANGLE ANGLE THEOREMS

- Author:
- Rachel Turner, Tim Brzezinski

## WORDS TO KNOW:

## ANGLE RELATIONSHIPS REVIEW:

Use the diagram of *g||h*, with transversal *f*, to answer the questions.
A pair of corresponding angles is ______________.

Angle 2 is _________ angle 8

A pair of same-side interior angles is _____________.

## REMEMBER!

Which statements regarding the diagram are true? Check all that apply.

## INTERIOR AND EXTERIOR ANGLE THEOREMS

*Be sure to change the locations of the triangle's WHITE VERTICES each time before you drag the slider!!!*TYPE YOUR ANSWERS AND CLICK THE CHECK YOUR ANSWER BOX.

## INTERIOR AND EXTERIOR ANGLE THEOREM QUESTIONS:

1. What geometric transformations took place in the applet above for interior angles? CHECK ALL THAT APPLY

2. When working with the triangle's interior angles, did any of these transformations change the measures of the blue or green angles?

3. From your observations, what is the sum of the measures of the interior angles of
*any triangle? *

4. When working with the triangle's exterior angles, did any of these transformations change the measures of the green or gray angles?

5. From your observations, what is the sum of the measures of the exterior angles of
*any triangle? *

## ANOTHER WAY TO FIND THE SUMS OF INTERIOR ANGLES OF A TRIANGLE

## THIRD ANGLE THEOREM

## THIRD ANGLE THEOREM

6. Describe how can you find the measure of angle C?

We use this information to help us prove that the sum of the interior angles of a triangle is _______ degrees.

Determine the measure of the missing angles.

## EXTERIOR ANGLE THEOREMS

## EXTERIOR ANGLE THEOREM QUESTIONS:

7. What geometric transformations took place in the applet above? CHECK ALL THAT APPLY

8. As you move the vertices on the applet, what do you notice about the remote angles and the exterior angle?

9. What is the relationship between the exterior angle and ONE of the remote angles?

What is the measure of ∠XBC?

*m*∠XBC =*m*∠BAC +*m*∠BCA- 3
*p*– 6 =*p*+ 4 + 84 - 3
*p*– 6 =*p*+ 88 - 2
*p*– 6 = 88 - 2
*p*= 94

*m*∠XBC = _______ °

## ANALYZING THE RELATIONSHIPS BETWEEN INTERIOR AND EXTERIOR ANGLES OF TRIANGLES

Analyze the diagram to complete the statements.
The *m*∠MXN is __________ *m*∠YZX.

The *m*∠LZX is __________ *m*∠ZYX + *m*∠YXZ.

The *m*∠MYL is ________ 180° − *m*∠ZYX.