LESSON 8.4: Similarity in Right Triangles

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LESSON 8.4 Similarity in Right Triangles

• OBJECTIVES
• To determine and use relationships in similar
  right triangles

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Vocabulary and Key Concepts

the positive number m such that

• The geometric mean of two positive numbers a
  and b is ____________________________.

Example Find the geometric mean of 4 16.
If , then m 2 (4)(16) m 2
64 m 8
SV
Thus, the geometric mean of 4 and 16 is 8.
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FINDING THE GEOMETRIC MEAN

• Find the geometric mean of 3 and 12.

m2 36
SV
m 6
NOTE We use only the positive square root,
since length/distance is measured in positive
numbers.
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Theorem 8-3 The altitude (perpendicular
segment) 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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• Corollary 1 to 8-3 The length of the altitude
  to the hypotenuse of a right triangle is
  _________________________________________________
  _______________________________________.
• Corollary 2 to 8-3 The altitude to the
  hypotenuse of a right triangle ___________________
  ________________________________________________
  _____________________________ ____________________
  ____________________________________________.

the geometric mean of the
lengths of the segments of the hypotenuse.
separates the hypotenuse so that the length of
each leg of a triangle is the geometric mean of
the length of the adjacent hypotenuse segment and
the length of the hypotenuse.
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FINDING DISTANCE

• At a golf course, Maria Teehawk drover her
  ball 192 yards straight toward the cup. Her
  brother, G.O. Teehawk drove his ball 240 yard,
  but not toward the cup. The diagram shows the
  results. Find x and y, their remaining
  distances from the cup.
• Next, find the distance between Marias ball
  and G.0.s ball.

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Work Space
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Final Checks for Understanding

1. How can we use relationships in similar right
   triangles in real-life?
2. What is the geometric mean of two numbers?
3. Find the geometric mean of 15 and 20.
4. Why do we use only the positive square root when
   finding the geometric mean of two numbers?

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Homework Assignment