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Bell work:

Learn how to solve problems involving ratios and proportions, identify similarity in shapes, and find scale factors for similar figures.

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Bell work:

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  1. Bell work: • Find your name; that is your new seat. Say hi to your face partner(sitting across from you) and your shoulder partner(sitting next to you)

  2. Today’s Goal(s) • Solve Problems involving Proportions • Identify Similarity in different shapes

  3. 7.1: Ratios and Proportions

  4. If a baseball team had the following win-loss record for the years shown, which year(s) were they most successful?

  5. Ratios • A ratio is comparing two qualities using division; ratios are generally written in one of three ways: , a:b, or “a to b” • In nearly all cases, ratios are written in simplest terms. • You can also have extended ratios, which compare three or more numbers. These are usually written as a:b:c

  6. The Bonsai Bald Cypress tree is a miniature version of a full sized tree. They measure 15 inches tall. There is a Florida Bald Cypress tree named the Senator which stands 118 FEET tall. • What is the ratio of the height of a Bonsai to the Senator?

  7. With your shoulder partner

  8. Using extended ratios • What is the extended ratio we can write? • If the perimeter of the triangle is 98, what would the length of the longest side be? • Compare your answer with your face partner when finished.

  9. Magic 11 • Each member of your group acts as if they are playing rock, paper, scissors. However, instead of playing one of those, they will hold out a number 0 through 5. • The goal of the game is to get the sum of your whole group’s fingers to equal 11. Keep playing until you get it! Once you hit that target, someone in your group picks a new number. Repeat.

  10. Notes • An equation involving ratios is called a proportion. The first and last numbers in the proportion are known as extremes, whereas the middle numbers are called the means. • i.e., 2:3=4:6 is a proportion. 2 and 6 are the extremes, and 3 and 4 are the means. • Just like with ratios, we can have an extended proportion, such as 2:3=4:6=8:12 • Cross Product Property: In a proportion, the product of the means equals the product of the extremes. • i.e., 2 x 6 should be equal to 3 x 4

  11. More Notes

  12. In this picture, x:6 = y:7. • Therefore, x:y would equal…what?

  13. Break Time

  14. 7.2: Similar Polygons

  15. Similar Figures are figures which have the exact same shape, but not necessarily the same size. This is shown with the symbol ~ • All the corresponding sides will be in the same ratio, as shown above. The simplified form of this ratio is called the scale factor, and we could say the scale factor of ABCD to GHIJ is AB:GH, or BC:HI, etc.

  16. MNP ~ SRT • What are the pairs of congruent angles? • What is the extended proportion of the side ratios?

  17. Is JKLM ~ TUVW? If so, find the scale factor

  18. Is ABC ~ EFD? If so, find the scale factor

  19. Are these two shapes similar?

  20. Homework: • Section 7.1, page 436: 9-12, 16, 17, 19, 23, 24 • Section 7.2, pages 444-445: 9, 10, 12, 13, 17

  21. Section 7.1, page 436

  22. Section 7.2Pages 444-445

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