1. Legs Hypotenuse Pythagorean Triples
9.1 Pythagorean Theorem
Legs
Hypotenuse
Pythagorean Triples

2. The Pythagorean Theorem is probably the most famous mathematical relationship. In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

3. A set of three nonzero whole numbers a, b, and c such that a2 + b2 = c2 is called a Pythagorean triple.

4. Example 1: Using the Pythagorean Theorem
Find the value of x. Give your answer in simplest radical form.

5. Example 2A: Crafts Application
Randy is building a rectangular picture frame. He wants the ratio of the length to the width to be 3:1 and the diagonal to be 12 centimeters. How wide should the frame be? Round to the nearest tenth of a centimeter.

6. Check It Out! Example 2B
What if...? According to the recommended safety ratio of 4:1, how high will a 30-foot ladder reach when placed against a wall? Round to the nearest inch.

7. Example 3A: Identifying Pythagorean Triples
Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

8. Example 3B: Identifying Pythagorean Triples
Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.
Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

9. The converse of the Pythagorean Theorem gives you a way to tell if a triangle is a right triangle when you know the side lengths.

10. You can also use side lengths to classify a triangle as acute or obtuse.

11. To understand why the Pythagorean inequalities are true, consider ∆ABC.

12. Example 4A/B: Classifying Triangles
Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
5, 7, 10
Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
5, 8, 17

13. Lesson Quiz: Part I

14. Lesson Quiz: Part II
2. Find the value of x.
3. An entertainment center is 52 in. wide and 40 in. high. Will a TV with a 60 in. diagonal fit in it? Explain.

15. Lesson Quiz: Part III
4. What type of triangle could you form with sides of length 4”, 7” and 12” ?
NOT a Triangle
5. Tell if the measures 7”, 11”, and 15” can be the
side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
< OBTUSE

16. Lesson Quiz: Part IV
6. Given two legs of a Rt triangle are 4 and 8
Find the length of the hypotenuse in reduced radical form (RRF)