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Ratios in Similar Polygons

Ratios in Similar Polygons. Geometry (Holt 7-1) K. Santos. Similar Polygons. Similar Figures—have the same shape but not necessarily the same size

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Ratios in Similar Polygons

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  1. Ratios in Similar Polygons Geometry (Holt 7-1) K. Santos

  2. Similar Polygons Similar Figures—have the same shape but not necessarily the same size Two polygons are similar polygons if and only if their corresponding angles are congruentand their corresponding side lengths are proportional.

  3. Similar Polygons A 6 B M 15 N 120 110 110 120 10 4 10 25 C D 12 P 30 O

  4. Similar Polygons Corresponding congruent angles: < A < N < B < M< C < P< D < O Corresponding sides proportional: = = = = = = = = = scale factor or similarity ratio Similarity Statement: ABCD ~ NMPO order of letters makes a difference

  5. Similar Triangles R X 12 3 4 Y 15 S T 5 9 Z Corresponding congruent angles: < R < Y < T < X < S < Z Corresponding sides proportional: = = which all reduce to

  6. Example—Are the polygons similar? Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. A E 15 16 20 18 D 12 C 24 B F Identify pairs of congruent angles: <A <D <B <E <C <F Compare the corresponding sides: = = = = = = Similarity ratio:DEF

  7. Example If YXZ, find the value of m. Y A m 40 B 12 C X 30 Z Find the scale factor: = Then write a proportion using the scale factor and corresponding sides. = 5m = 80 m = 16

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