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# 7 - similar figures

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### 7 - similar figures

1. 1. Similar Figures(Not exactly the same, but pretty close!)
2. 2. Let’s do a little review workbefore discussing similar figures.
3. 3. Congruent Figures• In order to be congruent, two figures must be the same size and same shape. ≅
4. 4. Similar Figures• Similar figures must be the same shape, but their sizes may be different. ≅
5. 5. Similar Figures ≅ This is the symbol that means “similar.”These figures are the same shape but different sizes. ≅
6. 6. SIZES• Although the size of the two shapes can be different, the sizes of the two shapes4must differ by a factor. 2 6 6 3 1 3 ≅ 2
7. 7. SIZES• In this case, the factor is x 2. 4 2 3 3 ≅ 6 6 1 2
8. 8. SIZES• Or you can think of the factor as 2. 4 2 3 3 ≅ 6 6 1 2
9. 9. Enlargements• When you have a photograph enlarged, you make a similar photograph. ≅ X3
10. 10. Reductions• A photograph can also be shrunk to produce a slide. 4 ≅
11. 11. Determine the length of the unknown side. 1512 ≅ 4 ? 3 9
12. 12. These triangles differ by a factor of 3. 15 3= 5 1512 ≅ 4 ? 3 9
13. 13. Determine the length of the unknown side. ? 24 ≅ 24
14. 14. These dodecagons differ by a factor of 6. ? = 12 2 x6 24 ≅ 24
15. 15. Sometimes the factor between 2 figures is not obvious and some calculations are necessary.12 15 ≅ 8 10 18 12 ?=
16. 16. To find this missing factor, divide 18 by 12.12 15 ≅ 8 10 18 12 ?=
17. 17. 18 divided by 12 = 1.5
18. 18. The value of the missing factor is 1.5.12 15 ≅ 8 10 18 12 1.5 =
19. 19. When changing the size of a figure, will the angles of the figure also change? ? 4070 70 ? ?
20. 20. Nope! Remember, the sum of all 3angles in a triangle MUST add to 180 degrees. If the size of the angles were 40 increased, 40 the sum would exceed 180 degrees.70 70 70 70
21. 21. We can verify this fact by placing the smaller triangle inside the larger triangle. 40 4070 70 70 70
22. 22. The 40 degree anglesare congruent. 40 70 70 70 70
23. 23. The 70 degree anglesare congruent. 40 40 70 70 70 70
24. 24. The other 70 degreeangles are congruent. 4 40 70 7070 70 70
25. 25. Find the length of the missing side. 50 30 ? 6 40 8
26. 26. This looks messy. Let’stranslate the two triangles. 50 30 ?6 40 8
27. 27. Now “things” are easier to see. 50 30 ?6 40 8
28. 28. The common factor betweenthese triangles is 5. 50 30 ?6 40 8
29. 29. So the length ofthe missing side is…?
30. 30. That’s right! It’s ten! 50 30 106 40 8
31. 31. Similarity is used to answer real life questions. • Suppose that you wanted to find the height of this tree.
32. 32. Unfortunately all that you have is a tapemeasure, and you aretoo short to reach the top of the tree.
33. 33. You can measure the length of the tree’s shadow. 10 feet
34. 34. Then, measure the length of your shadow. 10 feet 2 feet
35. 35. If you know how tall you are,then you can determine how tall the tree is. 6 ft 10 feet 2 feet
36. 36. The tree must be 30 ft tall. Boy, that’s a tall tree! 6 ft 10 feet 2 feet
37. 37. Similar figures “work” just like equivalent fractions. 30 5 66 11
38. 38. These numerators anddenominators differ by a factor of 6. 30 6 5 6 66 11
39. 39. Two equivalent fractions are called a proportion.30 566 11
40. 40. Similar Figures• So, similar figures are two figures that are the same shape and whose sides are proportional.
41. 41. Practice Time!
42. 42. 1) Determine the missing side of the triangle. ? 5 93  4 12
43. 43. 1) Determine the missing side of the triangle. 15 5 93  4 12
44. 44. 2) Determine the missing side of the triangle.6 6 36 36  4 ?
45. 45. 2) Determine the missing side of the triangle.6 6 36 36  4 24
46. 46. 3) Determine the missing sides of the triangle. 39 ? 33  ? 824
47. 47. 3) Determine the missing sides of the triangle. 39 13 33  11 824
48. 48. 4) Determine the height of the lighthouse.8  ? 2.5 10
49. 49. 4) Determine the height of the lighthouse.8  32 2.5 10
50. 50. 5) Determine the height of the car. ?3  5 12
51. 51. 5) Determine the height of the car. 7.23  5 12
52. 52. THE END!