8-86th 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 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.

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

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°

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”

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 5-11

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 12-18

• If still more time, work on Accelerated Math.