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Chapter 7 Section 2 Similar Polygons

Chapter 7 Section 2 Similar Polygons. Objectives . Students will be able to identify and apply similar polygons. Essential Understanding. You can use ratios and proportions to decide whether two polygons are similar and to find unknown side lengths of similar figures. Similar Figures.

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Chapter 7 Section 2 Similar Polygons

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  1. Chapter 7 Section 2 Similar Polygons

  2. Objectives Students will be able to identify and apply similar polygons

  3. Essential Understanding You can use ratios and proportions to decide whether two polygons are similar and to find unknown side lengths of similar figures.

  4. Similar Figures Have the same shape but not necessarily the same size Is similar to is abbreviated by ~ symbol Two Polygons are similar if corresponding angles are congruent and the corresponding sides are proportional

  5. Writing Similarity Statements Like congruence statements, the order matters so if two figures are similar, their corresponding parts should be in the same order If ΔABC ~ ΔDEG then <A ~ <D and AB ~ DE

  6. Extended Proportions Use when three or more ratios are equal AB = BC = CD = ADGH HI IJ GJ Scale Factor: ratio of corresponding linear measurements to two similar figures (ratio of corresponding sides in simplest form)

  7. Example 1 What are the pairs of congruent angles if ΔABC ~ ΔRST? What is the extended proportion for the ratios of corresponding sides for ΔABC ~ ΔRST?

  8. Are the Polygons Similar? If so write a similarity statement and the scale factor

  9. Are the Polygons Similar? If so write a similarity statement and the scale factor

  10. Are the Polygons Similar? If so write a similarity statement and the scale factor

  11. Finding Lengths • ABCD ~ EFGD • What is the value of x? • What is the value of y?

  12. Finding Lenghts

  13. Using Similarity Your class is making a poster for a rally. The poster’s design is 6in. high by 10 in. wide. The space allowed for the poster is 4 ft high by 8ft wide. What are the dimensions for the largest poster that will fit in the space? What if the dimensions of the largest space was 3 ft high by 4 ft wide?

  14. Using Similarity

  15. Scale Drawing All lengths are proportional to their corresponding actual lengths Scale: ratio that compares each length in the scale drawing to the actual length Where have you seen a scale?

  16. The diagram shows a scale drawing of the Golden Gate Bridge. The distance between the two towers is the main span. What is the actual length of the main span of the bridge if it is 6.4 cm in the drawing?

  17. Homework Pg. 444 # 9 – 24, 32, 47 18 Problems

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