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Understanding Geometric Mean and Altitudes Concept

Learn how to find the geometric mean between two numbers with cross products and identify similar triangles using altitudes. Practice calculating geometric means and solving for triangle proportions.

stephenmartinez
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Understanding Geometric Mean and Altitudes Concept

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  1. Geometric Mean and Altitudes Concept 51

  2. Concept

  3. Find the geometric mean between 2 and 50. Let x represent the geometric mean. Definition of geometric mean Cross products Take the positive square root of each side. Simplify. Answer: The geometric mean is 10. Example 1

  4. 12 is the geometric mean between 8 and what number? Definition of geometric mean Cross products Divide each side by 8. Answer: The other number is 18. Example 1

  5. Write a similarity statement identifying the three similar triangles in the figure. Separate the triangles into two triangles along the altitude. ~ ΔEFH ~ ΔFGH ΔEGF Example 2

  6. Write a similarity statement identifying the three similar triangles in the figure. Example 2

  7. Concept

  8. Lets look at the Proportional statements for each set of similar triangles. ΔEGF ~ ΔFGH ~ΔEFH ΔEGF ~ ΔFGH ΔFGH ~ ΔEFH ΔEGF ~ ΔEFH

  9. Concept

  10. Find c, d, and e. Example 3

  11. Find e to the nearest tenth. A. 13.9 B. 24 C. 17.9 D. 11.3 Example 3

  12. Find the length of XZ. Example 4

  13. AIRPLANES Ajetliner has a wingspan, BD, of 211 feet. The segment drawn from the front of the plane to the tail, at point E.If AE is 163 feet, what is the length of the aircraft to the nearest tenth of a foot? A. 68.3 ft B. 231.3 ft C. 273.1 ft D. 436.1 ft Example 4

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