2. Converse of the Pythagorean Theorem 9.3 c =  10 c =  5

3. Converse of the Pythagorean Theorem 9.3 Chapter 9 Right Triangles and Trigonometry Section 9.3 Converse of the Pythagorean Theorem USE THE CONVERSE OF THE P YTHAGOREAN T HEOREM USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE

4. Converse of the Pythagorean Theorem 9.3 THEOREM A B C USE THE CONVERSE OF THE P YTHAGOREAN T HEOREM THEOREM 9.5 Converse of the Pythagorean Theorem c 2 = a 2 + b 2 b a c In a triangle, if c 2 = a 2 + b 2, then the triangle is a right triangle  ABC is a right Triangle 

5. Converse of the Pythagorean Theorem 9.3 THEOREM A B C USE THE CONVERSE OF THE P YTHAGOREAN T HEOREM THEOREM 9.6 c 2 < a 2 + b 2 In a triangle, if c 2 < a 2 + b 2, then the triangle is acute  ABC is acute b a c

6. Converse of the Pythagorean Theorem 9.3 THEOREM A C B b a c USE THE CONVERSE OF THE P YTHAGOREAN T HEOREM THEOREM 9.7 c 2 > a 2 + b 2 In a triangle, if c 2 > a 2 + b 2, then the triangle is obtuse  ABC is obtuse

7. Converse of the Pythagorean Theorem 9.3 Converse of the Pythagorean Theorem C ONCEPT S UMMARY c 2 < a 2 + b 2  Acute c 2 = a 2 + b 2  Right c 2 > a 2 + b 2 Obtuse USE THE CONVERSE OF THE P YTHAGOREAN T HEOREM A B C b a c A B C b a c A C B b a c

8. Converse of the Pythagorean Theorem 9.3 USE THE CONVERSE OF THE P YTHAGOREAN T HEOREM With c as the longest side, fill in c 2 = a 2 + b 2

9. Converse of the Pythagorean Theorem 9.3 USE THE CONVERSE OF THE P YTHAGOREAN T HEOREM With c as the longest side, fill in c 2 = a 2 + b 2 15 2 = 12 2 + 9 2 225 = 144 + 81 225 = 225 The triangle is a right triangle

10. Converse of the Pythagorean Theorem 9.3 USE THE CONVERSE OF THE P YTHAGOREAN T HEOREM 169  149 Not a Right Triangle 180 = 180 Right Triangle

11. Converse of the Pythagorean Theorem 9.3 USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Make sure they can form a triangle, then compare c 2 to a 2 + b 2

12. Converse of the Pythagorean Theorem 9.3 USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Make sure they can form a triangle, then compare c 2 to a 2 + b 2

13. Converse of the Pythagorean Theorem 9.3 USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE Make sure they can form a triangle, then compare c 2 to a 2 + b 2 Compare c 2 with a 2 + b 2 Substitute Multiply c 2 = a 2 + b 2 Since c 2 = a 2 + b 2, the triangle is a right triangle

14. Converse of the Pythagorean Theorem 9.3 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