8-8 6 th grade math Similar Figures

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.

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.

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.

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 d x f a 8 c ab ~ de ac df 6 ~ 3 8 X 24 ÷ 6 = 4 df = 4

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 ̊ 1 03 ̊ 30 ̊ x ̊ 180 – ( ) 180 – 133 = 47°

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 = ( 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 36÷ 9 = 4 KN = 4”

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.

Independent Practice Complete problems Copy original problem first. Show all work! If time, complete Mixed Review: If still more time, work on Accelerated Math.