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Altitude in Right Triangle: Geometric Mean & Proportions

Explore the Similar Right Triangles Theorem and find proportions of the parts of a right triangle's hypotenuse. Discover how altitudes create similar triangles and geometric means with detailed examples. Solve for x, y, and z using set up proportions. Homework help with problems from page 531 to 534.

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Altitude in Right Triangle: Geometric Mean & Proportions

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  1. 9.1 Similar Right Triangles

  2. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right triangle.

  3. Since this is true We have proportions.

  4. Since this is true The legs of the right triangle are the Geometric mean to the part of the hypotenuse and the whole hypotenuse.

  5. Find x and y Set up the proportions

  6. Find x and y Set up the proportions

  7. Find x and y Set up the proportions

  8. Since this is true The altitude is also a Geometric mean.

  9. Recapping The Altitude is the geometric mean of the parts of the hypotenuse A leg of the Original Right Triangle is the geometric mean of part of the hypotenuse touching it and the whole hypotenuse.

  10. Find x, y and z

  11. Find x, y and z

  12. Solve for x, y and z

  13. Solve for x, y and z

  14. Solve for x, y and z

  15. Solve for x, y and z

  16. Solve for x, y and z

  17. Homework Page 531 – 534 # 11 – 33,41,42

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