Mastering Triangle Properties: Formal Proofs & Classification Examples

1. Section 3-3Parallel Lines and the Triangle Angle-Sum Theorem

2. 1 1 2 3 3 2 Activity #1 1 2 3

3. 1 2 3 1 Activity #2 2 3

4. 2 3 D E Formal Proof A 1 Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180˚. 4 5 B C

5. Formal Proof A Triangle Exterior Angle Theorem: The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. 2 D 4 1 3 B C

6. Classify by Angles Classifying Triangles 60˚ 60˚ 60˚ Obtuse Acute Equiangular Right Classify by Sides Equilateral Isosceles Scalene

7. Example 1 x 67˚ 48˚

8. Example 2 z 70˚ x y

9. Example 3:classify by angles and sides 5 2 120˚ 4

10. Example 4: 125˚ X

11. Example 5: A triangle with a 90˚ angle has sides that are 3 cm, 4 cm, and 5 cm long. Classify the triangle by its angles and sides.

12. Example 6: y 70˚ 42˚

13. Example 7: 90˚ 76˚ x

14. Example 8: 2x + 28 4x 32˚

15. Example 9: 5x + 40 10x 3x − 4

16. Example 10: x 125˚ 160˚