1. OBJECTIVE I will use the Pythagorean Theorem to find missing sides lengths of a RIGHT triangle.

2. leg - sides adjacent to right angle leg hypotenuse - longest side - opposite of right angle Right angle - one 90 0 angle The Right Triangle

3. What is the Pythagorean Theorem? The theorem that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse. Used to find the missing side of a triangle when two sides are given *Only works with right triangles The formula is: - where a and b are the legs of a triangle and c is the hypotenuse of the triangle

4. 1. Square both legs 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16

5. 2. Count the total squares 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16 9 + 16 = 25

6. 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16 9 + 16 = 25 3. Put that number of squares on the hypotenuse 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25

7. 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16 9 + 16 = 25 4. Count the number of squares that touch the hypotenuse. 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25 # = 5

8. 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16 9 + 16 = 25 5.That number is the length of the hypotenuse. 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25 # = 5 Length = 5

9. Using the Pythagorean Theorem –Start with the formula –Determine what numbers go with the variables a, b, and c a and b are the legs c is the hypotenuse –Substitute the numbers into the formula and solve

10. Example - Finding the Hypotenuse a = 6 b = 8 c = ? Equation Substitute Exponents Add Find Square Root Length must be positive

11. Guided Practice Find the length of the hypotenuse.

12. Finding a Leg Find the leg of a right triangle with one leg that is 9cm and a hypotenuse of 12cm. Equation Substitute Subtract 81 from both sides Find Square Root Length is Positive The other leg is 12cm.

13. Guided Practice Find the leg of a right triangle with one leg that is 12cm and a hypotenuse of 20cm.

14. Independent Practice 1.Find the hypotenuse of a right triangle with legs of 3in and 4in. 2.Find the leg of a right triangle with a leg of 15ft and a hypotenuse of 25 feet.