The document discusses similar figures in geometry. It defines similar figures as two figures that are the same shape but not necessarily the same size, as the corresponding sides are proportional. It provides examples of determining missing side lengths of similar figures using scale factors. It also notes that angles of similar figures are congruent, and scale factors can be used to solve real-world problems involving similar triangles.

1. Bell Ringer Which number completes this proportion? (15 / 35) = (x / 84) x = 30 x = 33 x = 36 x = 39 A person that weighs 150 pounds on the Earth will weigh 25 pounds on the Moon. How much will a 90-pound person weigh on the Moon? 10 lb 12 lb 15 lb 20 lb

2. Similar Figures (Not exactly the same, but pretty close!)

3. Let’s do a little review work before discussing similar figures.

4. Congruent Figures In order to be congruent, two figures must be the same size and same shape.

5. Read IT Correctly spell and pronounce the term Write IT Write the definition of the term in your own words Draw IT Represent the term through examples and visuals

7. Similar Figures Similar figures must be the same shape, but their sizes may be different.

9. Similar Figures This is the symbol that means “similar.” These figures are the same shape but different sizes.

10. SIZES Although the size of the two shapes can be different, the sizes of the two shapes must differ by a factor. 3 3 2 1 6 6 2 4

11. SIZES In this case, the factor is x 2. 3 3 2 1 6 6 2 4

12. SIZES Or you can think of the factor as 2. 3 3 2 1 6 6 2 4

13. Enlargements When you have a photograph enlarged, you make a similar photograph. X 3

14. Determine the length of the unknown side. 12 9 15 4 3 ?

15. These triangles differ by a factor of 3. 12 9 15 4 3 ? 15 3= 5

16. Determine the length of the unknown side. 4 2 24 ?

17. These dodecagons differ by a factor of 6. 4 2 24 ? 2 x 6 = 12

18. Sometimes the factor between 2 figures is not obvious and some calculations are necessary. 18 12 15 12 10 8 ? =

19. To find this missing factor, divide 18 by 12. 18 12 15 12 10 8 ? =

20. 18 divided by 12 = 1.5

21. The value of the missing factor is 1.5. 18 12 15 12 10 8 1.5 =

22. When changing the size of a figure, will the angles of the figure also change? ? ? ? 70 70 40

23. Nope! Remember, the sum of all 3 angles in a triangle MUST add to 180 degrees. If the size of the angles were increased, the sum would exceed 180 degrees. 70 70 40 70 70 40

24. We can verify this fact by placing the smaller triangle inside the larger triangle. 70 70 40 70 70 40

25. 70 70 70 70 40 The 40 degree angles are congruent.

26. 70 70 70 70 70 40 40 The 70 degree angles are congruent.

27. 70 70 70 70 70 40 4 The other 70 degree angles are congruent.

28. Find the length of the missing side. 30 40 50 6 8 ?

29. This looks messy. Let’s separate the two triangles. 30 40 50 6 8 ?

30. Now “things” are easier to see. 30 40 50 8 ? 6

31. The common factor between these triangles is 5. 30 40 50 8 ? 6

32. So the length of the missing side is…?

33. That’s right! It’s ten! 30 40 50 8 10 6

34. Similarity is used to answer real life questions. Suppose that you wanted to find the height of this tree.

35. Unfortunately all that you have is a tape measure, and you are too short to reach the top of the tree.

36. You can measure the length of the tree’s shadow. 10 feet

37. Then, measure the length of your shadow. 10 feet 2 feet

38. If you know how tall you are, then you can determine how tall the tree is. 10 feet 2 feet 6 ft

39. The tree must be 30 ft tall. Boy, that’s a tall tree! 10 feet 2 feet 6 ft

40. Similar figures “work” just like equivalent fractions. 5 30 66 11

41. These numerators and denominators differ by a factor of 6. 5 30 66 11 6 6

42. Two equivalent fractions are called a proportion. 5 30 66 11

43. Similar Figures So, similar figures are two figures that are the same shape and whose sides are proportional.

44. Practice Time!

45. 1) Determine the missing side of the triangle. 3 4 5 12 9 ?

46. 1) Determine the missing side of the triangle. 3 4 5 12 9 15

47. 2) Determine the missing side of the triangle. 6 4 6 36 36 ?

48. 2) Determine the missing side of the triangle. 6 4 6 36 36 24

49. 3) Determine the missing sides of the triangle. 39 24 33 ? 8 ?

50. 3) Determine the missing sides of the triangle. 39 24 33 13 8 11

51. 4) Determine the height of the lighthouse. 2.5 8 10 ?

52. 4) Determine the height of the lighthouse. 2.5 8 10 32

53. 5) Determine the height of the car. 5 3 12 ?

54. 5) Determine the height of the car. 5 3 12 7.2

55. Homework Page 291 #9, 11, 12 Page 295-296 #8, 10, 12

56. Scale factor = new value old value . 8cm 12cm 5cm 7.5cm New value = Old value New value = Old value 12 = 3 or 1.5 8 2 Can you see the relationship between the two scale factors? 8 = 2 12 3 Scale factor? Scale factor?

57. Using scale factor 9cm a Enlarge with scale factor 3 b 15cm a = 9 x 3 = 27cm SF = new/old = 9/27 = ⅓ What will the scale factor be? b = 15 x ⅓ = 15 ÷ 3 = 5cm OR reciprocal of 3 = ⅓

58. THE END!