1. THE PYTHAGOREAN THEOREM AND AREA OF A TRIANGLE

2. Warm – Up!! Good Morning! As you walk in, get your calculator and pick up your guided notes from the podium. Go ahead and label your triangle based on the definitions below (be sure to fill in the definitions too!):  Hypotenuse – the side of a right triangle opposite the right angle and the longest side.  Legs – the sides of a right triangle that are not the hypotenuse.

3. 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 legs.

4. IF I AM GIVEN 2 SIDES OF A RIGHT TRIANGLE MAKE UP THE SIDES OF PYTHAGOREAN TRIPLE, HOW DO YOU FIND THE MISSING SIDE? There are 2 possible scenarios: 1. You are given both legs of the right triangle and need to solve for the hypotenuse. 2. You are given one leg and one hypotenuse and need to solve for the other leg.

5. EXAMPLE 1: USE THE PYTHAGOREAN THEOREM TO FIND THE HYPOTENUSE. 68x²x² 36 + 64 = x ² 100= x ²

6. EXAMPLE 2: USE THE PYTHAGOREAN THEOREM TO FIND THE HYPOTENUSE.

7. PYTHAGOREAN TRIPLES  A Pythagorean Triple is a set of 3 positive integers or whole numbers that satisfies the Pythagorean theorem.

8. IS IT A PYTHAGOREAN TRIPLE? 33, 4, and 5 221, 28, and 35 330, 72, and 91 114, 48, and 50 yes no yes

9. EXAMPLE 3: FIND THE MISSING LEG x3 5² x ² + 9 = 25 x ² = 16

10. YOU TRY!! FIND THE MISSING LEG

11. FIND THE AREA WHEN GIVEN A LEG AND THE HYPOTENUSE 1. Find the other leg by plugging the known values into the Pythagorean Theorem. 2. Use the 2 legs in the formula for area of a triangle  A = ½BH

12. Find the perimeter of a triangle by adding the sides.  P = a + b + c, where a, b, and c are sides  Example:

13. FIND THE AREA OF THE TRIANGLE What is the formula for the area of a triangle? A = ½bh How will we find the height?

14. Find the Area of the Triangle

15. YOU TRY!! FIND THE AREA WHEN GIVEN A LEG AND A HYPOTENUSE. 8 16

16. YOU TRY!! FIND THE AREA WHEN GIVEN A LEG AND A HYPOTENUSE. 13 17