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Welcome to Math 6 Today’s subject is: Proportions and Similar Figures

Welcome to Math 6 Today’s subject is: Proportions and Similar Figures. Objectives for this lesson: Each student will:

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Welcome to Math 6 Today’s subject is: Proportions and Similar Figures

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  1. Welcome to Math 6 Today’s subject is: Proportions and Similar Figures

  2. Objectives for this lesson: Each student will: 1- Use proportions to determine if two figures are similar.2-Use proportions to make similar figures.3-Use proportions to find the length of corresponding sides of similar figures.

  3. Key Vocabulary Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.

  4. 10 21 Use ratios to determine if two figures are similar. 24

  5. 10 21 DE corresponds to RS.EF corresponds to SQQR corresponds to FD 24

  6. 10 21 24

  7. 10 21 24

  8. Similar figures have the same shape, but not necessarily the same size. Similar figures have corresponding sides and corresponding angles. The symbol ~ means “is similar to.” ABC ~ QRS.

  9. If two figures are similar, then their corresponding angles are congruent, and the lengths of the corresponding sides are proportional.

  10. To find out if triangles are similar, determine whether the ratios of the lengths of their corresponding sides are proportional. If the ratios are proportional, then the corresponding angles must have equal measures.

  11. Similar figures have two properties: The corresponding angles have equal measures. The lengths of the corresponding sides are in proportion.

  12. In figures with four or more sides, it is possible for the corresponding side lengths to be proportional and the figures to have different shapes. To find out if these figures are similar, first check that their corresponding angles have equal measures. 7 7 7 7

  13. When you know two figures are similar, you can find the measure of a missing side by setting up a proportion. Parallelogram ABCD ~ Parallelogram EFGH. Find the value of x.

  14. Create a proportion:

  15. Guided Practice

  16. Guided Practice #1 Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar. 4 9 12 20 6 3

  17. Guided Practice #2 Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar.

  18. Guided Practice #3 Use the properties of similarity to determine whether the figures are similar.

  19. Guided Practice #4 Use the properties of similarity to determine whether the figures are similar. y

  20. Guided Practice #5These two triangles are similar. Use a proportion to find the length of the missing side.

  21. Guided Practice #5 Notes to instructor Show how the measure of y = 4.

  22. Independent Practice

  23. Independent Practice #1Use the properties of similarity to determine whether the figures are similar. y

  24. Independent Practice #2 Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar.

  25. Independent Practice #3Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar.

  26. Independent Practice #4Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar.

  27. Independent Practice #5These two triangles are similar. Use a proportion to find the length of the missing side.

  28. Independent Practice #6These two triangles are similar. Use a proportion to find the length of the missing side.

  29. Independent Practice #7Use the properties of similarity to determine whether the figures are similar. y

  30. Independent Practice #8Write a proportion for corresponding sides which would make these similar figures. G

  31. Independent Practice #9Write a proportion for corresponding sides which would make these similar figures. Trapezoid EFGH ~ trapezoid MNOP

  32. Independent Practice #10Write a proportion for corresponding sides which would make these similar figures.

  33. Conclusion In this lesson we: 1- Used proportions to determine if two figures are similar.2-Used proportions to make similar figures.3-Used proportions to find the length of corresponding sides of similar figures.

  34. Assignments- • Complete the attached exercise entitled, “Worksheet 4.2: Proportions and Similar Figures.” • Look at Math website for more information about Proportions and similar figures. http://www.math.com/school/subject3/lessons/S3U3L2GL.html

  35. Assignments- 3. Here is one more website to check out for more information. This one actually has a quiz at the end. You can test yourself to find out how much of this you have retained. The website is http://studyjams.scholastic.com/studyjams/jams/math/geometry/similar-figures.htm

  36. See you next time! See you next time! See you next time! See you next time!

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