7.4 Similarity in Right Triangles

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7.4 Similarity in Right Triangles

• The altitude to the hypotenuse of a right
  triangle divides the triangle into two triangles
  that are similar to the original triangle and to
  each other.

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Geometric Mean

• The geometric mean of two positive numbers a and
  b is the positive number x that satisfies

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Find a Geometric Mean

• Find the geometric mean of 6 and 15.

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Corollary 1 to Theorem 7.3

• The length of the altitude to the hypotenuse of a
  right triangle is the geometric mean of the
  lengths of the segments of the hypotenuse.

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Corollary 2 to Theorem 7.3

• The altitude to the hypotenuse of a right
  triangle separates the hypotenuse so that the
  length of each leg of the triangle is the
  geometric mean of the length of the hypotenuse
  and the length of the segment of the hypotenuse
  adjacent to the leg.

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Using the Corollaries

• What are the values of x and y?

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More Practice!!!!!

• Homework Textbook p. 464 465 3 6, 9 21.