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Similarity in Right Triangles

Similarity in Right Triangles. 8.1. Are any triangles in the figure similar? If so…Why?. E. B. A. D. E. B. E. D. A. D. How could we set up the ratios of the sides?. E. B. E. D. A. D. Example 1: Identifying Similar Right Triangles.

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Similarity in Right Triangles

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  1. Similarity in Right Triangles 8.1

  2. Are any triangles in the figure similar? If so…Why? E B A D E B E D A D

  3. How could we set up the ratios of the sides? E B E D A D

  4. Example 1: Identifying Similar Right Triangles Write a similarity statement comparing the three triangles.

  5. Consider the proportion . In this case, the means of the proportion are the same number, and that number is the geometric mean of the extremes. The geometric meanof two positive numbers is the positive square root of their product. So the geometric mean of a and b is the positive number x such that , or x2 = ab.

  6. Example 2A: Finding Geometric Means Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. 4 and 25

  7. Example 2B: Finding Geometric Means Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. 5 and 30

  8. Example 3: Finding Side Lengths in Right Triangles Find x, y, and z. 62 = (9)(x) 6 is the geometric mean of 9 and x. x = 4 Divide both sides by 9. y is the geometric mean of 4 and 13. y2 = (4)(13) = 52 Find the positive square root. z2 = (9)(13) = 117 z is the geometric mean of 9 and 13. Find the positive square root.

  9. Example 3a Find u, v, and w. 92 = (3)(u) 9 is the geometric mean of u and 3. u = 27 Divide both sides by 3. w2 = (27 + 3)(27) w is the geometric mean of u + 3 and 27. Find the positive square root. v2 = (27 + 3)(3) v is the geometric mean of u + 3 and 3. Find the positive square root.

  10. You Try! Use Geometric mean of the ALTITUDE to find the missing distance! X BONUS…What is the height of the Cliff from the ground up?

  11. You Try Again! Find the geometric mean of the LEG to find the missing distance!

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