1. Example 1 1.What is the area of a square with a side length of 4 inches? x inches? 2.What is the side length of a square with an area of 25 in 2 ? x in 2 ? x x

2. Parts of a Right Triangle Which segment is the longest in any right triangle?

3. 7.1 Apply the Pythagorean Theorem Objectives: 1.To discover and use the Pythagorean Theorem 2.To use Pythagorean Triples to find quickly find a missing side length in a right triangle

4. The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

5. The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

6. The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

7. Example 2 The triangle below is definitely not a right triangle. Does the Pythagorean Theorem work on it?

8. Example 3 How high up on the wall will a twenty- foot ladder reach if the foot of the ladder is placed five feet from the wall?

9. Example 4: SAT In figure shown, what is the length of RS?

10. Example 5 What is the area of the large square?

11. Example 6 Find the area of the triangle.

12. Pythagorean Triples Pythagorean Triples Three whole numbers that work in the Pythagorean formulas are called Pythagorean Triples.

13. Example 7 What happens if you add the same length to each side of a right triangle? Do you still get another right triangle?

14. Example 8 What happens if you multiply all the side lengths of a right triangle by the same number? Do you get another right triangle?

15. Pythagorean Multiples Pythagorean Multiples Conjecture: If you multiply the lengths of all three sides of any right triangle by the same number, then the resulting triangle is a right triangle. In other words, if a 2 + b 2 = c 2, then (an) 2 + (bn) 2 = (cn) 2.

16. Pythagorean Triples Pythagorean Triples

17. Primitive Pythagorean Triples primitive Pythagorean triple A set of Pythagorean triples is considered a primitive Pythagorean triple if the numbers are relatively prime; that is, if they have no common factors other than 1. 3-4-55-12-137-24-258-15-17 9-40-4111-60-6112-35-3713-84-85 16-63-6520-21-2928-45-5333-56-65 36-77-8539-80-8948-55-7365-72-97

18. Example 9 Find the length of one leg of a right triangle with a hypotenuse of 35 cm and a leg of 28 cm.

19. Example 10 Use Pythagorean Triples to find each missing side length.

20. Example 11 A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top of the ladder slips down 4 feet, how many feet will the bottom slip out?