Chapter 7

• Scale Factor


  ratio of the lengths of 2 corresponding sides
• Spiraling pattern

  Every golden rectangle contains an infinite number of golden rectangles in a spiral pattern
• Facts about the golden rectangle

  1. All golden rectangles are similar 2. When a square is cut out, it creates another golden rectangle similar to the original
• Properties of proportions: a/b = c/d is equivalent to

  ad =bc, a/c = b/d, b/a = d/c, and a+b/b = c+d/d
• Means extremes property of proportions (cross products)

  If a/b = c/d, then ad (means) = bc (extremes)
• Proportion

  An equation stating that two ratios are equal
• Ratio

  Comparison of 2 quantities by division (a/b, a:b, a to b)
• Golden ratio?

  1 + √5 / 2
• If a/b = c/d = e/f = ... , then?

  a + c+ e + ... / b + d + f + ... = a/b
• When are two polygons similar?

  When their vertices can be paired so that:

  1. Corresponding angles are congruent
  2. Corresponding sides are proportional (all sides are in the same ratio)
• What is the symbol for similar?

  ~
• AA ~ Postulate


  If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar
• What is the tip for writing proofs when you have to use AA ~ Postulate?


  Look for triangles inside of triangles, you probably have to prove them similar if it's not obvious
• SAS ~ Theorem


  If one angle of a triangle is congruent to an angle of another triangle, and the sides that include those angles are in proportion, then the triangles are similar
• SSS ~ Theorem


  If the sides of 2 triangles are in proportion, then the triangles are similar
• Triangle Angle Bisector Theorem


  If a ray bisects the angle of a triangle, then it divides the opposite side into segments proportional to the other sides
• If 3 or more parallel lines intersect 2 traversals, then it divides them proportionally
• Triangle Proportionality Theorem


  If a line parallel to one side of a triangle intersects the other 2 sides, then it divides those sides proportionally