SIMILAR POLYGONS

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CHAPTER 7

• SIMILAR POLYGONS

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SECTION 7-1

• Ratios and Proportions

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• RATIO a comparison of two numbers, a and b,
  represented in one of the following ways
• a b a or a to b
• b

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• EQUIVALENT RATIOS two ratios that can both be
  named by the same fraction.
• 48 and 7 14

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• PROPORTION is an equation that states that two
  ratios are equivalent.
• a b c d a c
• b d

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• EXTREMES the first and last terms
• a b c d
• a and d are extremes

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• MEANS the second and third terms
• a b c d
• b and c are means

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• CROSS PRODUCTS the product of the extremes
  equals the product of the means.
• ad bc

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SECTION 7-2

• Properties of Proportions

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• TERMS the four numbers a, b, c, and d that are
  related in the proportion.

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Properties of Proportions

• a/b c/d is equivalent to
• ad bc
• a/c b/d
• b/a d/c
• (a b)/b (c d)/d
• If a/b c/d e/f , then
• (ace)/(bdf) a/b

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SECTION 7-3

• Similar Polygons

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• SCALE DRAWING is a representation of a real
  object.
• SCALE is the ratio of the size of the drawing
  to the actual size.

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• SIMILAR figures that have the same shape

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• CORRESPONDING ANGLES angles in the same
  position in congruent or similar polygons.

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• CORRESPONDING SIDES sides in the same position
  in congruent or similar polygons.

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• SIMILAR POLYGONS figures having all
  corresponding angles congruent and the measures
  of all corresponding sides are in the same
  proportion. The symbol for similarity is ?

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Scale Factor

• - The ratio of the lengths of two corresponding
  sides

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SECTION 7-4

• A Postulate for Similar Triangles

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AA Similarity

• If two angles of one triangle are congruent to
  two angles of another triangle, then the
  triangles are similar.

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SECTION 7-5

• Theorems for Similar Triangles

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SAS Similarity

• If an angle of one triangle is congruent to an
  angle of another triangle and the sides including
  those angles are in proportion, then the
  triangles are similar.

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SSS Similarity

• If the sides of two triangles are in proportion,
  then the triangles are similar.

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SECTION 7-6

• Proportional Lengths

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Theorem 7-3

• If a line parallel to one side of a triangle
  intersects the other two sides, then it divides
  those sides proportionally.

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Corollary

• If three parallel lines intersect two
  transversals, then they divide the transversals
  proportionally.

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Theorem 7-4

• If a ray bisects an angle of a triangle, then it
  divides the opposite side into segments
  proportional to the other two sides.

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END