8-8 6 th grade math similar figures. objective to use proportions to solve problems involving...
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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 fa b h gd 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 ~ deac df6 ~ 38 X24 ÷ 6 = 4df = 4
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How to Solve Missing Angles of Similar Figures
1) Locate corresponding angles.
2) If finding a triangle’s missing angle, remember triangles angles add to 180°. If finding a rectangle’s missing angle, remember rectangles add to 360°.
3) Add the angles and subtract from either 180 (triangle) or 360 (rectangle).
Triangles are similar. abc ~ def 103 ̊ 103̊
30̊ x ̊
180 – (103 + 30)180 – 133 = 47°
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Try It!
Quadrilateral KLMN ~ to quadrilateral GHIJ.
1) m K∠
2) HI
3) KN
H I 110° L 2” M 9” 3” 110°
K 70°N G 12” J
1) m K = 360 - (110 + 110 + 70 + x)∠ 360 – 270 = 702) HI =LM = KL 2 = 3HI GH x 9
18 ÷ 3 = 6HI = 6”3) KNGJ = GH 12 = 9KN KL x 336 ÷ 9 = 4 KN = 4”
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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.