c = 10

1. c = 10 c = 5

2. USE THE CONVERSE OF THE PYTHAGOREAN THEOREM USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Chapter 9Right Triangles and Trigonometry Section 9.3 Converse of the Pythagorean Theorem

3. USE THE CONVERSE OF THE PYTHAGOREAN THEOREM THEOREM c a A b B C THEOREM 9.5 Converse of the Pythagorean Theorem In a triangle, if c2 = a2 + b2, then the triangle is a right triangle ABC is a right Triangle  c2 = a2 + b2

4. USE THE CONVERSE OF THE PYTHAGOREAN THEOREM THEOREM C b a A B c THEOREM 9.6 In a triangle, if c2 < a2 + b2, then the triangle is acute ABC is acute c2 < a2 + b2

5. USE THE CONVERSE OF THE PYTHAGOREAN THEOREM THEOREM c a B b A C THEOREM 9.7 In a triangle, if c2 > a2 + b2, then the triangle is obtuse ABC is obtuse c2 > a2 + b2

6. USE THE CONVERSE OF THE PYTHAGOREAN THEOREM • Converse of the Pythagorean Theorem CONCEPT SUMMARY c c a a A b b c a C B b B C A B A C c2 < a2 + b2  Acute c2 = a2 + b2  Right c2 > a2 + b2 Obtuse

7. USE THE CONVERSE OF THE PYTHAGOREAN THEOREM With c as the longest side, fill in c2 = a2 + b2

8. USE THE CONVERSE OF THE PYTHAGOREAN THEOREM With c as the longest side, fill in c2 = a2 + b2 152 = 122 + 92 225 = 144 + 81 225 = 225 The triangle is a right triangle

9. USE THE CONVERSE OF THE PYTHAGOREAN THEOREM 169  149 Not a Right Triangle 180 = 180 Right Triangle

10. USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Make sure they can form a triangle, then compare c2 to a2 + b2

11. USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Make sure they can form a triangle, then compare c2 to a2 + b2

12. USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Make sure they can form a triangle, then compare c2 to a2 + b2 Compare c2 with a2 + b2 Substitute Multiply c2 = a2 + b2 Since c2 = a2 + b2, the triangle is a right triangle

13. USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE 12, 16, 20 400 = 400 The triangle is a right triangle 1681 > 1664 The triangle is obtuse