8-8 6th grade math

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8-86th grade math

• Similar Figures

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Objective

• To use proportions to solve problems involving
  similar figures
• Why? To know how to solve missing sides or
  lengths of triangles, rectangles, etc. that are
  similar in size.

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California State Standards

• NS 1.3 Use proportions to solve problems
  (e.g find the length of a side of a polygon
  similar to a known polygon)
• MR 2.4 Use a variety of methods, such as words,
  numbers, symbols, diagrams, to explain
  mathematical reasoning.

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Vocabulary

• Similar figures
• Figures that have the same shape but not the same
  size (congruent same size and shape)
• e
  f
• a b
• h
  g
• d c
• Rectangles abcd efgh or abcd efgh
  (similar to)
• ab ef cd gh bc fg da he
  (corresponding sides or lengths). Sides lengths
  change.
• ?a ?e ?b ?f ?c ? g ?d ? h
  (corresponding angles). Angles measurement
  always stay the same, no matter how the angles
  change.

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How to Solve Missing Sides of Similar Figures

• 1) Locate corresponding sides. Color coding each
  corresponding side might help you to see
  better.
• 2) Write a proportion. Corresponding sides make
  one ratio. (AC/DF)
• 3) Solve.
• A short cut may be to observe how the similar
  figure was enlarged or decreased and multiply
  or divide with that number.

• Triangles are similar. abc def
• b e
• 6 4 3
  2
• d x
  f
• a 8 c
• ab de
• ac df
• 6 3
• 8 X
• 24 6 4
• df 4

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How to Solve Missing Angles of Similar Figures

• Triangles are similar. abc def
• 103 103
• 30 x
• 180 (103 30)
• 180 133 47

• 1) Locate corresponding angles.
• 2) If finding a triangles missing angle,
  remember triangles angles add to 180. If
  finding a rectangles missing angle, remember
  rectangles add to 360.
• 3) Add the angles and subtract from either 180
  (triangle) or 360 (rectangle).

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Try It!

• H I
• 110
• L 2 M 9
• 3 110
• K 70N G 12 J
• 1) m? K 360 - (110 110 70 x)
• 360 270 70
• 2) HI
• LM KL 2 3
• HI GH x 9
• 18 3 6
• HI 6
• 3) KN
• GJ GH 12 9
• KN KL x 3
• 9 4
• KN 4

• Quadrilateral KLMN to quadrilateral GHIJ.
• m? K
• HI
• KN

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Objective Review

• To use proportions to solve problems involving
  similar figures

• Why? You now know how to solve missing sides or
  lengths of triangles, rectangles, etc. that are
  similar in size.
• Use proportions to find missing sides of similar
  figures.
• Write proportions with corresponding part of
  similar figures.

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Independent Practice

• Complete problems 5-11
• Copy original problem first.
• Show all work!

• If time, complete Mixed Review 12-18
• If still more time, work on Accelerated Math.