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Lesson 7-1

Lesson 7-1. Geometric Mean. The geometric mean between two numbers a and b is the positive number x where . Therefore x =. Try It:. Find the geometric mean of. Answer = 20. 1. 10 and 40. 2. 1 and 36. Answer = 6. 3. 10 and 20. Answer = 14.14. 4. 5 and 6.

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Lesson 7-1

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  1. Lesson 7-1 Geometric Mean Lesson 7-1: Geometric Mean

  2. The geometric mean between two numbers a and b is the positive number x where . Therefore x = . Try It: Find the geometric mean of . . . Answer = 20 1. 10 and 40 2. 1 and 36 Answer = 6 3. 10 and 20 Answer = 14.14 4. 5 and 6 Answer = 5.48 Answer = 9.94 5. 8.1 and 12.2 Lesson 7-1: Geometric Mean

  3. A B C How does this relate to geometry? Lesson 7-1: Geometric Mean

  4. If the altitude is drawn from the vertex of the 90° angle of a Right ▲ to its hypotenuse, then the two new ▲s formed are similar to the original ▲ andto each other.Example: ▲ABC ~ ▲DBA ~ ▲DAC Theorem 7.1 Lesson 7-1: Geometric Mean

  5. The " W " Pattern Lesson 7-1: Geometric Mean

  6. The Geometric Means Recall the three geometric means that you discovered from your Sketchpad activity. BUT FIRST . . . Lesson 7-1: Geometric Mean

  7. Re-label the Sides (as lengths) Lesson 7-1: Geometric Mean

  8. Geometric Mean #1 What is the proportion that uses f? f is the geometric mean of d and e. Lesson 7-1: Geometric Mean

  9. Geometric Mean #2 What is the proportion that uses b? b is the geometric mean of e and c. Lesson 7-1: Geometric Mean

  10. Geometric Mean #3 What is the proportion that uses a? a is the geometric mean of d and c. Lesson 7-1: Geometric Mean

  11. Put them all together Lesson 7-1: Geometric Mean

  12. The “W” Pattern W Lesson 7-1: Geometric Mean

  13. The measure of an altitude drawn from the vertex of the 90° angle of a Right ▲ to its hypotenuse is the geometric mean between the measures (lengths) of the two segments of the hypotenuse.Example: AD is the geometric mean of BD and DC. Theorem 7.2 Lesson 7-1: Geometric Mean

  14. Try it ! Given: d = 4 and e = 10 Find: a = ___ b = ___ c = ___ f = ___ Lesson 7-1: Geometric Mean

  15. Solution: Proportions Answers Lesson 7-1: Geometric Mean

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