1. The Pythagorean Theorem Objective: Find the length of a using the Pythagorean Theorem.

2. : Interesting fact: “The name of Pythagoras was selected for this theorem not because he discovered it - - the Pythagorean theorem or Pythagorean triples had been in use for centuries. -- but perhaps because Pythagoras was the first to prove the theorem.”

3. Mini Lab 1. Find the area of each square. 2. Use grid paper to cut out three squares with sides 3, 4, and 5 units. Form a right triangle with these squares. Compare the sum of the areas of the two smaller squares with the area of the larger square.

4. We use the when we want to know the remaining length of the side of a right triangle for which we already know two lengths. We use the Pythagorean Theorem when we want to know the remaining length of the side of a right triangle for which we already know two lengths. In a right triangle the 2 sides that form the right triangle are called. In a right triangle the 2 sides that form the right triangle are called legs. The side opposite the right angle is called the It is the longest side of the triangle. The side opposite the right angle is called the hypotenuse. It is the longest side of the triangle. The the relationship between the length of the and the length of the. The Pythagorean Theorem describes the relationship between the length of the hypotenuse and the length of the legs.

5. : The Pythagorean Theorem states: In a Right Triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a 2 + b 2 = c 2 a 2 + b 2 = c 2

6. Find the missing length in each right triangle. Example: Find the missing length in each right triangle. a 2 + b 2 = c 2 3 2 + 4 2 = C 2 9 + 16 = C 2 25 = c 2 5 = C Steps to find the hypotenuse: 1.Use the Pythagorean theorem. 2. Replace a with 3 and b with 4. 3. Square 3 and 4. 4. Add 5.Find the square root.

7. : Find the missing length in each right triangle. Example 2: Find the missing length in each right triangle. Steps: 1.Use Pythagorean Theorem. 2. Replace b with 8 and c with 12. 3.Square 8 and 12. 4.We “undo” the addition. We do this by subtracting 8 from each side. 5.Solve. 6.Find the square root. a 2 + b 2 = c 2 a 2 + 8 2 = 12 2 a 2 + 64 = 144 - 64 - 64 a 2 = 80 a = 8.94

8. Homework: Pythagorean Theorem