1. Geometry 7-2a Pythagorean Theorem

2. New Material

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

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

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

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

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

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

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 A C b B a c

10. Pythagorean = a brain?

11. Pythagorean Theorem This ONLY holds for right triangles

12. Pythagorean Theorem 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

13. Pythagorean Theorem - Example

19. Pythagorean Theorem - Practice

26. Geometry 7-2b Converse of the Pythagorean Theorem

27. Investigation – Work in groups of three Get your supplies –String –Three paper clips –Ruler –One piece of paper

28. Converse of the Pythagorean Theorem - Investigation

31. Theorem Converse of the Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. A C b B a c

32. Converse of the Pythagorean Theorem – Practice Problems

34. Converse of Pythagorean

35. Example

37. Converse of the Pythagorean Theorem – Practice Problems

39. Practice

41. Converse of the Pythagorean Theorem – Practice Problems

43. Homework Pages 361 -364 10 – 30 even, 40, 48, 78, 80