Chapter 7.3 Notes: Use Similar Right Triangles

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Chapter 7.3 Notes Use Similar Right Triangles

• Goal You will use properties of the altitude of
  a right triangle.

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• Theorem 7.5
• 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.
• Ex.1 Identify the similar triangles in the
  diagram.

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• Identify the similar triangles. Then find the
  value of x.
• Ex.2 Ex.3

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• Geometric Mean
• Theorem 7.6 Geometric Mean (Altitude) Theorem
• In a right triangle, the altitude from the right
  angle to the hypotenuse divides the hypotenuse
  into two segments.
• The length of the altitude is the geometric mean
  of the lengths of the two segments.

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• Ex.4 Find the value of the variable.

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• Theorem 7.7 Geometric Mean (Leg) Theorem
• In a right triangle, the altitude from the right
  angle to the hypotenuse divides the hypotenuse
  into two segments.
• The length of each leg of the right triangle is
  the geometric mean of the lengths of the
  hypotenuse and the segment of the hypotenuse that
  is adjacent to the leg.

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• Ex.5 Find the value of y. Write your answer in
  simplest radical form.
• Ex.6 Solve for x and y.
• x
• y
• 4
  5

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• Ex.7 Solve for x and y.
• 4
• x y
  12
• Ex.8 Solve for x, y, and z.
• x
• y 12
  16

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• Ex.9 The diagram below shows a cross-section of
  a swimming pool. What is the maximum depth of the
  pool?