1. Lesson Plan Lesson Plan for grades 9-12 Erica Papa

2. 1. Title Page Title Page 2. Table of contents Table of contents 3. Where did the Pythagorean Theorem come from? Where did the Pythagorean Theorem come from? 4. Pythagoras Pythagoras 5. Pythagorean Theorem equation Pythagorean Theorem equation 6. Can you label the triangle? Can you label the triangle? 7. Leading to Pythagorean Triples Leading to Pythagorean Triples 8. Pythagorean Triples Pythagorean Triples 9. Example 1 Example 1 10. Example 2 Example 2 11. To the Quiz To the Quiz 12. Question #1 Question #1 13. Question #2 Question #2 14. Question #3 Question #3 15. Question #4 Question #4 16. Question #5 Question #5 17. Find Homework Sheet Find Homework Sheet

3. Table of contents

4.  The Egyptians knew of this concept, as it related to 3, 4, 5 right triangles, long before the time of Pythagoras. It was Pythagoras, however, who generalized the concept and who is attributed with its first geometrical demonstration. Thus, it has become known as the Pythagorean Theorem. Table of contents

5. "In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.“ This relationship can be stated as: For any RIGHT TRIANGLE Table of contents

6. b c a a, b are legs c is the hypotenuse (c is across from the hypotenuse) leg hypotenuse leg Table of contents

7.  There are certain sets of numbers that have a very special property in relation to the Pythagorean Theorem. Not only do these numbers satisfy the Pythagorean Theorem, but any multiples of these numbers also satisfy the Pythagorean Theorem. Click here to find out! Table of contents

8. For example: the numbers 3, 4, and 5 satisfy the Pythagorean Theorem. If you multiply all three numbers by 3 ( 9, 12, and 15 ), these new numbers ALSO satisfy the Pythagorean theorem! 5 3 4 Table of contents

9. A B C 9m 12m x a b c c 2 = a 2 +b 2 x 2 = 81+144 x 2 = 225 x=15 Answer: 15 m = Find x. Table of contents

10. A triangle has sides 6, 7 and 11. Is it a right triangle? c 2 = a 2 +b 2 11 2 ? 6 2 +7 2 121? 36+49 121≠ 85 Let a = 6, b = 7 and c = 11. The longest side MUST be the hypotenuse, so c = 11. Now, check to see if the Pythagorean Theorem is true. Since the Pythagorean Theorem is NOT true, this triangle is NOT a right triangle.

11. Table of contents

12. Find x X= 15 X= 7 X= 26 X= 24 Table of contents

13. The lengths of the perpendicular sides of a right angled triangle 12 cm. and 16 cm. Then find the length of hypotenuse. X 12 cm 16 cm Find X X= 144 X= 20 X= 192 X= 32 Table of contents

14. To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond? Choose: 22 meters 53 meters 75 meters 41 meters Table of contents

15. Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point? Choose: X= 3 X= 4 X= 4.5 X= 4 Table of contents

16. How far up a wall will an 11m ladder reach, if the foot of the ladder must be 4m from the base of the wall? Find X X= 15.4 m X= 14.5 m X= 10.2 m X= 4 m Table of contents

17.  Back to Question #1 Back to Question #1  Back to Question #2 Back to Question #2  Back to Question #3 Back to Question #3  Back to Question #4 Back to Question #4  Back to Question #5 Back to Question #5  I finished the quiz! I finished the quiz! Table of contents

18.  Back to Question #1 Back to Question #1  Back to Question #2 Back to Question #2  Back to Question #3 Back to Question #3  Back to Question #4 Back to Question #4  Back to Question #5 Back to Question #5  I finished the quiz! I finished the quiz! Table of contents

19. Click the right triangle to print off the page for your homework and hand it in tomorrow to be graded. Table of contents

20. Back to find my homework!