8-4 Similarity in Right Triangles

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8-4Similarity in Right Triangles

• One Key Term
• One Theorem
• Two Corollaries

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• Draw a diagonal across your index card.
• On one side of the card use a ruler to draw the
  altitude of the right triangle from the corner of
  the index card perpendicular to the diagonal.
• Cut out the
• three triangles,
• examine them

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Theorem 8-3

• Altitude Similarity Theorem
• 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.

C
A
B
D
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Vocabulary

1. Geometric Mean

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1 Finding the Geometric Mean

• Find the geometric mean of 15 and 20.

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Purpose of the Geometric Mean

1. The geometric mean can give a meaningful
   "average" to compare two companies.
2. The use of a geometric mean "normalizes" the
   ranges being averaged, so that no range dominates
   the weighting.
3. The geometric mean applies only to positive
   numbers.2
4. It is also often used for a set of numbers whose
   values are meant to be multiplied together or are
   exponential in nature, such as data on the growth
   of the human population or interest rates of a
   financial investment.

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Corollary 1 to Theorem 8-3

• 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.

C
A
B
D
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Corollary 2 to Theorem 8-3

• 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 adjacent
  hypotenuse segment and the length of the
  hypotenuse.

C
A
B
D
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Similarity in Right Triangles
Find the values of x and y in the following right
triangle.
 
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You Try One!!!
Find the values of x and y in the following right
triangle.
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2
4

• Solve for x and y.

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x
y
4
x
y
12
y
x
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