9'1 Notes

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9.1 Notes

• Similar Right Triangles

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9.1 Notes

• Use a straightedge to draw ONE diagonal of the
  index card.
• Cut along the diagonal.

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9.1 Notes

• What terms describe the resulting triangles?
• Right
• Scalene
• Congruent
• Similar

4
9.1 Notes

• On one triangle label the right angle C, the
  smaller of the two acute angles A, and the other
  angle B. Label the angles on both the front and
  back of the card.

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9.1 Notes

• On the other triangle only label angles A and B.
  Label the angles on both the front and back of
  the card.

6
9.1 Notes

• An altitude of a triangle is a line segment from
  a vertex perpendicular to the opposite side.

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9.1 Notes

• Using the triangle that does not have the right
  angle labeled, draw the altitude from the right
  angle to the hypotenuse.

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9.1 Notes

• Now label the right angle C and the point where
  the altitude intersects the hypotenuse D. You are
  going to cut along the altitude so label the
  points on each side of the altitude. Label the
  angles on both the front and back of the card.

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9.1 Notes

• Now cut along the diagonal so that you have
  three triangles.
• What terms describe the resulting triangles?
• Right
• Scalene
• Similar

10
9.1 Notes

• Theorem 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.

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9.1 Notes

• Arrange your three similar triangles on your
  desk so that they are in the same orientation
  (facing the same way).

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9.1 Notes

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9.1 Notes

• Which angle on the small triangle corresponds to
  angle C on the large triangle?
• Which angle on the large triangle corresponds to
  angle C on the medium-size triangle?
• Which angle on the medium-size triangle
  corresponds to angle D on the small triangle?

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9.1 Notes

• Which side on the large triangle corresponds to
  side BD on the small triangle?
• Which side on the large triangle corresponds to
  side AC on the medium-size triangle?
• Which side on the medium-size triangle
  corresponds to side CD on the small triangle?

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9.1 Notes
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9.1 Notes
20
9.1 Notes

• Given is an altitude of right triangle ?MNO.
• Draw the three similar triangles in the same
  orientation.

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9.1 Notes

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9.1 Notes