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Similar to TechMathI - 6.2 - Similarity examples
TechMathI - 6.2 - Similarity examples
- 1. Similar Figures (Notexactly the same, but pretty close!)
- 2. Let’s do alittle review work before discussing similar figures.
- 3. Congruent Figures Inorder to be congruent, two figures must be the same size and same shape.
- 4. Similar Figures Similarfigures must be the same shape, but their sizes may be different.
- 5. Similar Figures Thisis the symbol that means “similar.” These figures are the same shape but different sizes.
- 6. SIZES Although thesize 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
- 7. SIZES In thiscase, the factor is x 2. 3 3 2 1 6 6 2 4
- 8. SIZES Or youcan think of the factor as 2. 3 3 2 1 6 6 2 4
- 9. Enlargements When youhave a photograph enlarged, you make a similar photograph. X 3
- 10. Reductions A photographcan also be shrunk to produce a slide. 4
- 11. Determine the lengthof the unknown side. 12 9 15 4 3 ?
- 12. These triangles differby a factor of 3. 12 9 15 4 3 ? 15 3= 5
- 13. Determine the lengthof the unknown side. 4 2 24 ?
- 14. These dodecagons differby a factor of 6. 4 2 24 ? 2 x 6 = 12
- 15. Sometimes the factorbetween 2 figures is not obvious and some calculations are necessary. 18 12 15 12 10 8 ? =
- 16. To find thismissing factor, divide 18 by 12. 18 12 15 12 10 8 ? =
- 17. 18 divided by12 = 1.5
- 18. The value ofthe missing factor is 1.5. 18 12 15 12 10 8 1.5 =
- 19. When changing thesize of a figure, will the angles of the figure also change? ? ? ? 70 70 40
- 20. 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
- 21. We can verifythis fact by placing the smaller triangle inside the larger triangle. 70 70 40 70 70 40
- 22. 70 70 7070 40 The 40 degree angles are congruent.
- 23. 70 70 7070 70 40 40 The 70 degree angles are congruent.
- 24. 70 70 7070 70 40 4 The other 70 degree angles are congruent.
- 25. Find the lengthof the missing side. 30 40 50 6 8 ?
- 26. This looks messy. Let’s translate the two triangles. 30 40 50 6 8 ?
- 27. Now “things” areeasier to see. 30 40 50 8 ? 6
- 28. The common factorbetween these triangles is 5. 30 40 50 8 ? 6
- 29. So the lengthof the missing side is…?
- 30. That’s right! It’sten! 30 40 50 8 10 6
- 31. Similarity is usedto answer real life questions. Suppose that you wanted to find the height of this tree.
- 32. Unfortunately all thatyou have is a tape measure, and you are too short to reach the top of the tree.
- 33. You can measurethe length of the tree’s shadow. 10 feet
- 34. Then, measure thelength of your shadow. 10 feet 2 feet
- 35. If you knowhow tall you are, then you can determine how tall the tree is. 10 feet 2 feet 6 ft
- 36. The tree mustbe 30 ft tall. Boy, that’s a tall tree! 10 feet 2 feet 6 ft
- 37. Similar figures “work”just like equivalent fractions. 5 30 66 11
- 38. These numerators anddenominators differ by a factor of 6. 5 30 66 11 6 6
- 39. Two equivalent fractionsare called a proportion. 5 30 66 11
- 40. Similar Figures So,similar figures are two figures that are the same shape and whose sides are proportional.
- 41.
- 42. 1) Determine themissing side of the triangle. 3 4 5 12 9 ?
- 43. 1) Determine themissing side of the triangle. 3 4 5 12 9 15
- 44. 2) Determine themissing side of the triangle. 6 4 6 36 36 ?
- 45. 2) Determine themissing side of the triangle. 6 4 6 36 36 24
- 46. 3) Determine themissing sides of the triangle. 39 24 33 ? 8 ?
- 47. 3) Determine themissing sides of the triangle. 39 24 33 13 8 11
- 48. 4) Determine theheight of the lighthouse. 2.5 8 10 ?
- 49. 4) Determine theheight of the lighthouse. 2.5 8 10 32
- 50. 5) Determine theheight of the car. 5 3 12 ?
- 51. 5) Determine theheight of the car. 5 3 12 7.2
- 52.