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Similar Figures and Solving Proportions

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Learn how to solve proportions using cross multiplication and explore the concept of similar figures having congruent angles and proportional sides.

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Similar Figures and Solving Proportions

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  1. Similar Figures Notes

  2. Solving Proportions Review • Before we can discuss Similar Figures we need to review how to solve proportions…. • Any ideas?

  3. Solving Proportions • Solving Proportions: You must cross multiply and solve for the missing value. • x • 35 • 2 • 5 • = • 2(35) • = • 5x • 70 • ____ • 5 • = • 5x • ____ • 5 • x = 14

  4. Proportions Practice • x = 14 • r = 28 • k = 45 • z = 9 • d = 66 • s = 72 • w = 36 • t = 12 • a = 24 • f = 14 • h = 18 • c =135 • z = 60 • k = 16 • n = 15

  5. Similar Figures (~)

  6. Similar Figures • Similar Figures: have the same shape but are not the same size. • Corresponding Angles of Similar Figures: are congruent. • Corresponding Sides of Similar Figures: are in proportion.

  7. Naming Similar Figures • When naming similar figures, list the corresponding sides and the angles in the same order. • For example, ∆ABC ~ ∆DEF Corresponding Angles • <A & <D • <A & <D • <A & <D Corresponding Sides • AB & DE • BC & EF • AC & DF

  8. Corresponding angles E B 82◦ 82◦ D 43◦ 55◦ F 43◦ 55◦ A C Corresponding sides Similar Figures (~) • Two Figures are Similar if: • Corresponding angles are congruent • Corresponding sides are in proportion

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