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Understanding Similar Polygons: Ratios, Proportions & More

Learn to identify and apply similar polygons using ratios, proportions, and corresponding sides and angles. Dive into scale factors, extended proportions, and problems to enhance your understanding.

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Understanding Similar Polygons: Ratios, Proportions & More

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  1. 7-2Similar Polygons Objective To identify and apply similar polygons

  2. Similar Figures: same shape but not necessarily the same size Abbreviate is similar to with the symbol . ~ You can use ratios and proportions to decide whether two polygons are similar and to find unknown side lengths of similar figures.

  3. Similar Polygons: And Corresponding sides are proportional. Notation: ∆ABC ~ ∆DEF Corresponding angles are congruent

  4. Extended Proportion When three or more ratios are equal, you can write an extended proportion:

  5. Scale Factor Ratio of corresponding linear measurements of two similar figures simplify The ratio of corresponding sides:

  6. What are the pairs of congruent angles? What is the extended proportion for the ratios of corresponding sides? You give it a shot.

  7. Are the polygons similar? If so, write a similarity statement and give the scale factor. Pairs of congruent angles: Compare the ratios of corresponding sides: Corresponding sides are notproportional, so the polygons are notsimilar.

  8. 10 cm 18 cm 12 cm 12 cm 12 cm 12 cm 1300 500 18 cm 500 1300 18 cm Similar Polygons: corresponding angles are congruent AND corresponding sides are proportional Does the AND matter? Congruent Angles Proportional sides No Yes Congruent Angles Proportional sides Yes No

  9. Similar Polygon Problems A 10 E B 12 x C D Given:ABCDE ~ JKLMN Find x and y 15 9 = x = 6 10 x J 15 N K y 15 = y = 18 10 12 9 y M L

  10. p. 444: 9-19 odd (include all ratios & diagrams)

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