1. Converse of the Pythagorean Theorem
Section 8-3

2. The Pythagorean Theorem States…
The squares of the sides of the legs of a right triangle have a sum equal to the square of the hypotenuse. c a b

3. Converse…(Theorem 8-3)
If the square of the largest side of a triangle is equal to the sum of the squares of the other two, then the triangle is a right triangle. b a
Then this is a right triangle c

4. Tell whether each is a right triangle.13 4 3 6 no
yes 5 12 17 15
yes 8

5. Some Common Right Triangles
3, 4, , 12, , 15, , 24, 25
6, 8, , 24, , 30, , 48, 50
9, 12, 15
12, 16, 20
15, 20, 25

6. Theorem 8-4
If the square of the largest side is greater than the sum of the squares of the other two sides, the triangle is obtuse c b
Then this is an obtuse triangle a

7. Theorem 8-5
If the square of the largest side is less than the sum of the squares of the other two sides, the triangle is acute c
Then this is an acute triangle b a

8. Examples:
If a triangle has the following measurements for its sides, will it be acute, obtuse, or right?
1.) 12, 14, 15 2.) 33, 44, 55 3.) 8, 16, 20
Acute
Right
Obtuse