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Warm Up 11/28/12

Warm Up 11/28/12. Turn to page 16 in your packet Answer both questions . You will have to think back on previous concepts to complete these problems! Think about our types of triangles. 10 minutes. End. Homework Check. Today’s Objective.

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Warm Up 11/28/12

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  1. Warm Up 11/28/12 • Turn to page 16 in your packet • Answer both questions. You will have to think back on previous concepts to complete these problems! • Think about our types of triangles 10 minutes End

  2. Homework Check

  3. Today’s Objective • Students will be able to apply similarity to the triangles formed when an altitude drawn to the hypotenuse of a right triangle to find missing lengths.

  4. Find the missing terms of this pattern 2,6, 18, (?), 162, (?) What are we doing to one term to get the next term? Multiplying by 3 This is an example of a geometric sequence

  5. Geometric Sequence • A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. • What was the common ratio of our pattern? • 2, 6, 18, 54, 162, 486

  6. Geometric Mean • Each term in a geometric sequence is the geometric mean of the two terms that it falls between. • For example, what is the geometric mean between 2 and 18? • 2, 6, 18, 54, 162, 486

  7. Geometric Mean • In symbols, we can write this as 2:6 = 6:18 or 2/6=6/18. • The two 6’s are called the means of the proportion and the 2 and the 18 are called the extremes. • If you look at the first equation we wrote, the sixes fall in the middle, like the mean, and the 2 and the 18 are on the outside, or extreme edges of the equation. • What are the extremes of 18 in our geometric sequence? • of 162?

  8. Finding Geometric Mean • Use cross multiplication to solve for geometric means • Example 1: Find the geometric mean of 2 and 8. • Example 2: Find the other extreme given a geometric mean of 10 and one extreme of 25. • Example 3: Find the geometric mean of 5 and 15. • Example 4: Find the other extreme given a geometric mean of 6 and one extreme of 3. • Example 5: Find the geometric mean of 5 and 8.

  9. Geometric Mean in Right Triangles • Find all the missing angles • What type of segment is DC? 60 30

  10. Geometric Mean in Right Triangles • An altitude from the right angle of a right triangles gives us three similar triangles • We know that the ratios of corresponding sides of similar triangles are proportional

  11. Page 18 4. Using ∆BDC and ∆CDA fill in the proportion: So DC must be the geometric mean of ___________ and ___________. 5. Using ∆BDC and ∆ABC fill in the proportion: So BC must be the geometric mean of ___________ and ___________. • Using ∆ADC and ∆ABC, fill in the proportion: So AC must be the geometric mean of ___________ and ___________.

  12. Mean Joe Green

  13. Example 1 – page 21

  14. Example 2

  15. Example 3

  16. Example 4

  17. Classwork • Page 22

  18. Homework • Page 23

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