1. CHAPTER 8 RIGHT TRIANGLES
8.3
THE CONVERSE OF THE PYTHAGOREAN THEOREM

2. THE PYTHAGOREAN THEOREM
Recall that the Pythagorean Theorem applies to all right triangles and shows that:
a² + b² = c² or
leg² + leg² = hypotenuse²

3. THEOREM 8-3
THEOREM 8-3
If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Theorem 8-3 is the converse of the Pythagorean Theorem and says that if the Pythagorean Theorem works for a triangle, then it is right.

4. EXAMPLES Tell whether a triangle with given sides lengths is right
20, 21, 29
9, 15, 15
7, 24, 25
20, 21, 30
10, 24, 26
Yes No

5. If a² + b² = c², then ∆ABC is right.
THEOREM 8-3
If a² + b² = c², then ∆ABC is right. B b a A C c

6. If a² + b² > c², then ∆ABC is acute.
THEOREM 8-4 B
If a² + b² > c², then ∆ABC is acute. b a A C c

7. If a² + b² < c², then ∆ABC is obtuse.
THEOREM 8-5 B
If a² + b² < c², then ∆ABC is obtuse. b a A C c

8. EXAMPLES Tell whether a triangle with the given side lengths is right, acute, or obtuse.
20, 21, 30
20, 21, 28
5, 6, 8
8, 15, 17
Obtuse
Acute
Right

9. CLASSWORK/HOMEWORK 8.3 Assignment
Pg. 296, Classroom Exercises 1-10 all
Pg. 297, Written Exercises 1-8, 11-14