Ratios, Proportions, and Similar Triangles

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Ratios, Proportions, and Similar Triangles
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Ratios

• Ratios are like fractions
• The ratio 14 means 1 part to 4 parts
• and is equivalent to the fraction
• (partpart)
• OR (partwhole, because there are 5 parts
  altogether)

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Ratio Word Problems

• Attach an X to each part of the ratio
• Write and solve an equation using the expressions
• The ratio of two complementary angles is 1 2.
  Find the angles.
• lt1 1x, lt2 2x
• 1x 2x 90
• 3x 90 x 30
• lt1 30, lt2 60
• The ratio of two supplementary angles is 4 1.
  Find the angles.
• The ratio of the angles of a triangle is 2 3
  7. Find the angles.

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A. Solving Proportions

• Cross multiply and set the products equal to each
  other
• Be sure to use FOIL when multiplying polynomials
• Solve for the variable

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B. Properties of proportions
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Similar Polygons
shape
size

• Example of similar triangles
• Their corresponding angles are _______________.
• Their corresponding sides are in a
  ___________________.
• This ratio is called a _______________ and in
  this case is ____.
• We show that they are similar with this
  statement ____________.

congruent
direct ratio
scale factor
21
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