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Similar Figures

Similar Figures. (Not always exactly the same, but pretty close!). Similar Figures. Similar figures must be the same shape, but their sizes may be different. Similar Figures. ~ This is the symbol that means “ similar. ” These figures are the same shape but different sizes. ~. SIZES.

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Similar Figures

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

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

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

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

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

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

  7. Reductions • A photograph can also be shrunk to produce a slide. x

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

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

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

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

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

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

  14. 18 divided by 12 = 1.5

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

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

  17. Nope! Remember, the sum of all 3 angles in a triangle MUST add to 180 degrees.If the size of theangles were increased,the sum would exceed180degrees. 40 40 70 70 70 70

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

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

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

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

  22. Try this… 50 30 ? 6 40 8

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

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

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

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

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

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

  29. If you know how tall you are, then you can determine how tall the tree is by making a proportion. 6 ft 10 feet 2 feet

  30. The tree must be 30 ft tall. 6 ft 10 feet 2 feet

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

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

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

  34. Transformations on the Coordinate Plane Transformations are movements of geometric figures. The preimage is the position of the figure before the transformation, and the image is the position of the figure after the transformation.

  35. Moving points • Rules can be given to move coordinates on a plane to create a transformation • Example: Using the following rule (x+1, y-2) what happens to the point (6, 8)? (6 + 1, 8 – 2) = (7, 6)

  36. Making two points the same Triangle ABC has coordinates A(1, 2), B(3, 5), C( 6, 8) Triangle EFG has coordinates E(3, 5), F(5, 8), G(8, 11) Write a rule to change the vertices of triangle ABC to the vertices of triangle EFG.

  37. Scale Factors of Perimeter and Area • Perimeter: The ratio of the perimeters is the same as the ratio of the sides. Scale factor is the same too! • Area: If the scale factor of the sides of two similar polygons is m/n, then the ratio of the areas is (m/n)^2. (You square each part of the ratio) • Example: Ratio of sides = ¾ Ratio of area = 9/16

  38. Homework • Page 38, #5 • Page 40, #11 • Page 41-42, #14-18, • Page 43, #20-25 • Page 44, #31 • Page 64, #9-18 • Page 65, #19-22 • Page 68, #25-28 • Page 69, #31a, b, c

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