1. Pythagorean Theorem: What does the Pythagorean Theorem say? Use it to find the missing side?

2. Essential Question: What is the relationship between the sides of a triangle?

3. Why? There are more than 100 unique proofs of the Pythagorean Theorem!!!!! Let’s look at a few: Proof # 1 Proof # 2 Proof #3

4. Find Missing Side

5. Radical, Dude!

6. Converse of Pythag:

7. Goldilocks & the 3 Bears

8. Goldilocks Theorem: In a Right Triangle, the Hypotenuse is Just Right In an obtuse triangle, the ‘hypotenuse’ will be too long! In an acute triangle, the ‘hypotenuse’ will be too short!

9. Using Goldilocks: A triangle has side lengths of 10, 12, and 15. Classify this triangle by its ANGLES.

11. Unit Essential Question: How do you calculate and utilize the perimeter and area of 2-dimensional figures?

12. Essential Question: How do you find the perimeter of a polygon?

13. Perimeter & Area Perimeter – The sum of the lengths of the sides of a polygon. Area – The number of square units enclosed by a figure.

15. Perimeter & Area

16. Application:

17. Finding Circumference

18. Area Postulates What do these mean? Do you agree?

19. Find the Area:

20. Rectangle? Can you change this shape into a rectangle?

21. Essential Question: How do you find the area of a polygon?

22. Area of a Rectangle? Draw a Rectangle with length 5 and height 3. How many square units does it enclose?

23. Area Formulas:

24. Parallelograms:

25. Areas of Parallelograms:

26. So, what is the Area formula? How are base & height related?!?!?

27. Find the Areas:

28. Trapezoid Area? How can you change this Trapezoid into a Rectangle?

29. Essential Question: How do you find the area of a polygon?

30. Area of a Trapezoid:

31. Rhombi & Kites WHY?

32. Find the Area of the Rhombus:

33. Regular Polygon, Find the Angles

34. Essential Question: How do you find the area of a polygon?

35. Radius & Apothem

36. Area Formula?

37. Area Formula:

38. Find the Area of this Regular Decagon:

39. π - What is pi? π

40. Essential Question: How do you find the circumference and arc lengths of circles?

41. Vocab:

42. Arcs:

43. Identifying Arcs

44. _________ Addition Postulates Segment Angle Area…

45. Find each arc:

46. Circumference

47. Turning Radius?

48. Bicycle

49. Arc Length What does this mean?

50. Find the Arc Lengths

51. Think… Draw a picture! Is it possible for two circles to have arcs with the same measure, but different arc lengths? Is it possible for two circles to have arcs with the same length, but different arc measures?

52. Area of a Circle – click hereclick here

53. Essential Question: How do you find the area of sectors and circles?

54. Pizza mmmm… How much more pizza is there in a 12” diameter pizza than a 10” diameter pizza?

55. Slice of Pizza… If your pizza has a 16” diameter and the pizza is cut into 8 slices, then how big is each slice?

56. Area of a Sector The measure of the arc is the measure of ∠ AOB. Why does this formula work?

57. Area of sector ZOM Leave the answer in terms of π.

58. Probability What is the probability of rolling doubles on a pair of dice? What is the probability of a random student in class being a female? On a monopoly board, what place do you have the greatest probability of landing upon?

59. Essential Question: How do you use area models to find probability?

60. Geometric Probability

61. Gnat on a ruler? A ruler has an electric current flowing from 3 to 7 inches. What is the probability of the gnat landing on a portion of the ruler where it will meet certain death?

62. Waiting for the bus…