The document discusses the converse of the Pythagorean theorem, which states that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. It further states that if the square of the longest side is less than the sum of the squares of the other two sides, the triangle is acute, and if it is greater than the sum of the squares, then the triangle is obtuse. Examples are provided to illustrate each case.

1. 8-3 The Converse of the Pythagorean Theorem

2. The Converse of the Pythagorean Theorem DON’T WRITE THIS! If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

3. The Converse of the Pythagorean Theorem If c 2 = a 2 + b 2 Then right

4. The Converse of the Pythagorean Theorem Example Is this a right triangle? 7 8  113

5. The Converse of the Pythagorean Theorem Example How about this one? 15 36 4  95

6. The Converse of the Pythagorean Theorem DON’T WRITE THIS EITHER! If the square of the length of the longest side of a triangle is less than the sum of the square of the lengths of the other two sides, then the triangle is acute .

7. The Converse of the Pythagorean Theorem If c 2 < a 2 + b 2 Then Acute

8. The Converse of the Pythagorean Theorem YOU KNOW WHAT TO DO! If the square of the length of the longest side of a triangle is greater than the sum of the square of the lengths of the other two sides, then the triangle is obtuse .

9. The Converse of the Pythagorean Theorem If c 2 > a 2 + b 2 Then Obtuse

10. The Converse of the Pythagorean Theorem Example Are these side from a right, acute, or obtuse triangle? 38, 77, 86

11. SPICSA page 297 2-14 even The Converse of the Pythagorean Theorem