8 1 Similarity in Right Triangles
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This document discusses theorems and corollaries about right triangles. It states that if an altitude is drawn to the hypotenuse of a right triangle, the two triangles formed are similar. It also states that the length of the altitude is the geometric mean between the segments of the hypotenuse, and each leg is the geometric mean between the hypotenuse and adjacent hypotenuse segment. Students are assigned homework problems involving finding geometric means and values of unknowns in right triangles.
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8 1 Similarity in Right Triangles
- 1. Chapter 8 Right Triangles 8-1 Similarity in Right Triangles
- 2. Geometric Mean If a, b, and x are positive numbers and 𝑎 𝑥 = 𝑥 𝑏 then x is called the geometric mean between a and b. Find the geometric mean between 22 and 55. 11 10
- 3. Simplifying Radicals • We will be leaving radicals in simplified radical form. • We will not be changing radicals to decimals. • Practice simplifying radicals and finding the geometric mean on the next slide and bring the answers to class tomorrow. (HW)
- 4. HW Part 1
- 5. Theorem 8-1 If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. A BC N ∆𝐴𝐵𝐶~∆𝐴𝐶𝑁~∆𝐶𝐵𝑁
- 6. Corollary 1 When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse. A BC N 𝐴𝑁 𝐶𝑁 = 𝐶𝑁 𝐵𝑁
- 7. Corollary 2 When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg. A BC N 𝐴𝐵 𝐴𝐶 = 𝐴𝐶 𝐴𝑁 and 𝐴𝐵 𝐵𝐶 = 𝐵𝐶 𝐵𝑁
- 8. HW Part 2 • Find the values of the unknowns. y w x z 6 18