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Understanding Altitude on Hypotenuse Theorems in Right Triangles

This lesson explores the Altitude on Hypotenuse Theorems, which state that drawing an altitude to the hypotenuse of a right triangle results in two smaller similar triangles. It highlights the relationship that the square of the altitude is equal to the product of the two segments of the hypotenuse. Several examples are provided to reinforce understanding, where students will calculate missing side lengths using the properties of altitude and hypotenuse. Homework problems for practice are also included to enhance learning.

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Understanding Altitude on Hypotenuse Theorems in Right Triangles

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  1. 9.3 Altitude-on-Hypotenuse Theorems

  2. If an altitude is drawn to the hypotenuse of a right triangle, then it forms similar triangles. x y h

  3. The square of the altitude is equal to the product of the two pieces of the hypotenuse. x h2=xy y h

  4. Example 1 Given: BD = 6, AB = 9 Find: BC A B C D

  5. Example 2 Given: BC = 16, AB = 4 Find: BD A B C D

  6. Example 3 Given: BD = 9, AB = 3 Find: AC A B C D

  7. Example 4 Given: BC = 12, AB = 4 Find: BD A B C D

  8. Example 5 Given: BD = 2√5, AB = 8 Find: AC A B C D

  9. Homework p. 379 1a, 2a, 3a,d, 4a,b, 5a, 8, 10-13

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