9.1 Similar Triangles

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9.1 Similar Triangles
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Similar Triangles

• In order for two triangles to be
• similar
• Their angles must be _____________
• Their ___________ sides must be ____________

congruent
corresponding
proportional
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Geometric Mean

• The Altitude of a triangle is the _____________
  segment from a _____________ to the ____________
  side.
• The Altitude is called the Geometric Mean.
• Draw a picture

perpendicular
vertex
opposite
B
D
C
A
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Theorem 9.1
altitude

• If the ______________ is drawn to the hypotenuse
  of a ___________ triangle, then the two triangles
  formed are ____________ to the ____________
  triangle and to each other.
• Draw a picture and write the three SIMILARITY
  STATEMENTS

right
similar
original
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Example 1

• A roof has a cross section that is a right
  triangle. The diagram shows the approximate
  dimensions of this cross section.
• a) Identify the similar triangles in the diagram.
• b) Find the height of h.

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Example 1 contd
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Theorem 9.2

• In a right triangle, the altitude from the
  _____________ angle to the ____________ divides
  the hypotenuse into two segments. The length of
  the altitude is the ___________ _____________ of
  the lengths of the two segments.
• In the diagram
• In other words

hypotenuse
right
mean
geometric
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Theorem 9.3
right

• In a right triangle, the altitude from the
  ___________ angle to the _____________ divides
  the hypotenuse into two segments. The length of
  each leg of the right triangle is the
  _________________ _________ of the lengths of
  the ____________ and the segment of the
  hypotenuse that is _____________ to the leg.
• In the diagram
• In other words

hypotenuse
geometric
mean
hypotenuse
adjacent
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Example 2

• Solve for the missing variable

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Independent Classwork

• Lets find b, c, and d.
• Then finish the Practice Problems from Yesterday.
• (Worksheet)