1. c = 10
c = 5

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

3. In a triangle, if c2 = a2 + b2, then the triangle is a right triangle
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
THEOREM
THEOREM 9.5 Converse of the Pythagorean Theorem
In a triangle, if c2 = a2 + b2, then the triangle is a right triangle A B C b a c
ABC is a right Triangle 
c 2 = a 2 + b 2

4. In a triangle, if c2 < a2 + b2, then the triangle is acute
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
THEOREM
THEOREM 9.6
In a triangle, if c2 < a2 + b2, then the triangle is acute A B C b a c
ABC is acute
c 2 < a 2 + b 2

5. In a triangle, if c2 > a2 + b2, then the triangle is obtuse
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
THEOREM
THEOREM 9.7
In a triangle, if c2 > a2 + b2, then the triangle is obtuse A C B b a c
ABC is obtuse
c 2 > a 2 + b 2

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

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

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

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

10. Triangle Inequality Theorem
Recall that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. AB + BC > AC AC + BC > AB AB + AC > BC

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

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

13. Since c2 = a2 + b2, the triangle is a right triangle
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

14. 12, 16, 20 USE SIDE LENGTHS TO CLASSIFY TRIANGLES
BY THEIR ANGLE MEASURE
12, 16, 20