1. Pythagorean Theorem
Geometry 7-2a

2. New Material

3. Supplies
Handout ( one of two )
Scissors
Compass
Ruler
Investigation

4. Investigation Each person start with one of the triangles.
Each triangle includes a square on its edge
Label the triangle legs a and b
Label the hypotenuse c
Investigation

5. Locate the center of the square on the longest leg by drawing the diagonals.
Label this point O
Investigation

6. Through point o, construct line j, perpendicular to the hypotenuse
Through point o, construct line k, parallel to the hypotenuse
Investigation

7. Cut out the smaller square, and the four parts of the larger square (divided by the lines j and k)
Investigation

8. Investigation What is the Pythagorean theorem?
Arrange the five pieces to cover the larger square
What is the Pythagorean theorem?
Investigation

9. Theorem The Pythagorean theorem
In a right triangle, the sum of the squares of the legs of the triangle equals the square of the hypotenuse of the triangle B c a A C b
Theorem

10. This ONLY holds for right triangles
Pythagorean Theorem

11. Pythagorean Theorem 3,4,5 5,12,13 8,15,17 7,24,25 Pythagorean Triples
Whole numbers that satisfy the Pythagorean theorem. ISTEP loves multiples of these.
3,4,5
5,12,13
8,15,17
7,24,25
Pythagorean Theorem

12. Pythagorean Theorem - Example

13. Pythagorean Theorem - Example

14. Pythagorean Theorem - Example

15. Pythagorean Theorem - Example

16. Pythagorean Theorem - Example

17. Pythagorean Theorem - Example

18. Pythagorean Theorem - Practice

19. Pythagorean Theorem - Practice

20. Pythagorean Theorem - Practice

21. Pythagorean Theorem - Practice

22. Pythagorean Theorem - Practice

23. Pythagorean Theorem - Practice

24. Pythagorean Theorem - Practice

25. Pages 361 – 364
10 – 20 even, 40, 80
Homework