1. CH. 4.1 APPLY TRIANGLE SUM PROPERTIES

2. VOCAB Interior Angles : angles inside the triangle (sum = 180) Exterior Angles: angles outside the triangle Interior angles exterior angle exterior angle exterior angle

3. CLASSIFYING BY SIDES SCALENEISOSCELES EQUILATERAL _____ CONGRUENT SIDES _____ CONGRUENT SIDES _____ CONGRUENT SIDES

4. CLASSIFYING BY SIDES SCALENEISOSCELES EQUILATERAL ____ CONGRUENT SIDES _____ CONGRUENT SIDES _____ CONGRUENT SIDES 0 2 3

5. CLASSIFYING BY ANGLES OBTUSE EQUIANGULAR _____ ACUTE ANGLES ACUTE _____ ACUTE ANGLES _____ ACUTE ANGLES RIGHT _____ ACUTE ANGLES

6. CLASSIFYING BY ANGLES OBTUSE EQUIANGULAR _____ ACUTE ANGLES ACUTE _____ ACUTE ANGLES _____ ACUTE ANGLES RIGHT _____ ACUTE ANGLES 3 2 2 3

7. THEOREM 4.1: TRIANGLE SUM THEOREM The sum of the measures of the interior angles of a triangle is ________. CA B m<A + m<B + m<C = ______

8. THEOREM 4.1: TRIANGLE SUM THEOREM The sum of the measures of the interior angles of a triangle is ________. CA B m<A + m<B + m<C = ______ 180

9. THEOREM 4.1: TRIANGLE SUM THEOREM EX. C A B m<A + m<B + m<C = 180 42 71 x

10. THEOREM 4.1: TRIANGLE SUM THEOREM EX. C A B m<A + m<B + m<C = 180 42 + 71 + x = 180 113 + x = 180 - 113 - 113 x = 67 42 71 x

11. THEOREM 4.2: EXTERIOR ANGLE THEOREM The MEASURE OF AN EXTERIOR ANGLE OF A TRIANGLE IS EQUAL TO THE SUM OF THE MEASURES OF THE TWO ________ ANGLES. C A B m<1 = m<__ + m<__ 1

12. THEOREM 4.2: EXTERIOR ANGLE THEOREM The MEASURE OF AN EXTERIOR ANGLE OF A TRIANGLE IS EQUAL TO THE SUM OF THE MEASURES OF THE TWO __________________ ANGLES. C A B m<1 = m<__ + m<__ nonadjacent A B 1

13. THEOREM 4.2: EXTERIOR ANGLE THEOREM EX. C A B m<1 = m<A + m<B 1 42 71

14. THEOREM 4.2: EXTERIOR ANGLE THEOREM EX. C A B m<1 = m<A + m<B m<1 = 42 + 71 m<1 = 113 1 42 71

15. EXAMPLE 3 C A B m<1 = m<A + m<B 3x - 9 x 73 D

16. EXAMPLE 3 C A B m<1 = m<A + m<B 3x – 9 = x + 73  move small x to big x - x -x 2x – 9 = 73  solve for x +9 +9 3 x – 9 = 2x = 82x = 41 so, 3(41) – 9 = 114 2 2 3x - 9 x 73 D

17. COROLLARY TO THE TRIANGLE SUM THEOREM THE ACUTE ANGLES OF A RIGHT TRIANGLE ARE ____________________. C A B m<A + m<B = ______

18. COROLLARY TO THE TRIANGLE SUM THEOREM THE ACUTE ANGLES OF A RIGHT TRIANGLE ARE ____________________. C A B m<A + m<B = ______ COMPLEMENTARY 90 = 90

19. COROLLARY TO THE TRIANGLE SUM THEOREM EX. C A B m<A + m<B = 90 x 27

20. COROLLARY TO THE TRIANGLE SUM THEOREM EX. C A B m<A + m<B = 90 27 + x = 90 - 27 - 27 x = 63 x 27