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1. Write a similarity statement comparing the two triangles. Simplify. 2.

1. Write a similarity statement comparing the two triangles. Simplify. 2. Solve each equation. 4. . ∆ ADB ~ ∆ EDC. 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.

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1. Write a similarity statement comparing the two triangles. Simplify. 2.

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  1. 1. Write a similarity statement comparing the two triangles. Simplify. 2. Solve each equation. 4. ∆ADB ~ ∆EDC

  2. 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 Let x be the geometric mean. x2 = (4)(25) = 100 Def. of geometric mean x = 10 Find the positive square root.

  3. 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 Let x be the geometric mean. x2 = (5)(30) = 150 Def. of geometric mean Find the positive square root.

  4. Check It Out! Example 2b Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. 10 and 30 Let x be the geometric mean. x2 = (10)(30) = 300 Def. of geometric mean Find the positive square root.

  5. W Z Example 1: Identifying Similar Right Triangles Write a similarity statement comparing the three triangles. Sketch the three right triangles with the angles of the triangles in corresponding positions. By Theorem 8-1-1, ∆UVW ~ ∆UWZ ~ ∆WVZ.

  6. You can use Theorem 8-1-1 to write proportions comparing the side lengths of the triangles formed by the altitude to the hypotenuse of a right triangle. All the relationships in red involve geometric means.

  7. 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.

  8. Check It Out! Example 3 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.

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