1. The Pythagorean Theorem
Section 8.1
The Pythagorean Theorem
And Its Converse

2. Pythagorean Theorem – In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs.
a2 + b2 = c2 c a b

3. Example 1
Example 2 c 12 6 8 b

4. Pythagorean Triples
These are side lengths that will come up frequently when dealing with right triangles.
3, 4, __
6, 8, __
9, 12, __
12, 16, __
15, 20, __ … 5
5, 12, __
10, 24, __
8, 15, __
7, 24, __ 13 10 26 15 20 17 25 25

5. 1. A right triangle has leg lengths 5 and , find the length of the hypotenuse.
Theorem 8-3 A triangle has side lengths 3, 2, and Is the triangle a right triangle? Show work. c 5

6. Theorem 8-3 If c2 > a2 + b2, then m∠C is greater than 90 and ∆ABC is obtuse. A triangle has sides of 7, 8, and 11.
Theorem 8-4 If c2 < a2 + b2, then m∠C is less than 90 and ∆ABC is acute. A triangle has sides of 6, 7, and 8.