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7-2 Similar Polygons

7-2 Similar Polygons. You used proportions to solve problems. Use proportions to identify similar polygons. Solve problems using the properties of similar polygons. Similar Polygons. Similar polygons have the same shape but not necessarily the same size. These figures are not similar.

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7-2 Similar Polygons

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  1. 7-2 Similar Polygons You used proportions to solve problems. • Use proportions to identify similar polygons. • Solve problems using the properties of similar polygons.

  2. Similar Polygons Similar polygons have the same shape but not necessarily the same size.

  3. These figures are not similar

  4. Page 469 Two polygons are similar if and only if • their corresponding angles are congruent • their corresponding side lengths are proportional.

  5. Geometry Symbols The symbol ~ means “is similar to”. The order of the letters in the similarity correspondence indicates the corresponding parts. It identifies the corresponding angles and sides. ABC ~ XYZ

  6. If ΔABC ~ ΔRST, list all pairs of congruent angles and write a proportion that relates the corresponding sides. Use the similarity statement. ΔABC ~ ΔRST Answer: Congruent Angles: A  R, B  S,C  T

  7. ABCDE ~ MNOPQ. Name all pairs of congruent corresponding angles, and write proportions using the pairs of corresponding sides. N O E A D M P C B Q

  8. Write the similarity correspondence. Name all pairs of congruent corresponding angles and write proportions using the pairs of corresponding sides. I 45 Q R 15 X F Y 53° 5 10 75 25 60 20 6 3 V W 37° 30 E 4 G T 90 S J H 8

  9. A.HGK  QPR B. C.K  R D.GHK  QPR If ΔGHK ~ ΔPQR, determine which of the following similarity statements is not true.

  10. Scale Factor If the scale factor is greater than 1, the similar figure is an enlargement. If the scale factor is less than 1, it is a reduction.

  11. Scale Factors See Example 2, page 470

  12. A.The two polygons are similar. Find x. Use the congruent angles to write the corresponding vertices in order. polygon ABCDE ~ polygon RSTUV Write a proportion to find x. Similarity proportion Cross Products Property Multiply. Divide each side by 4. Simplify.

  13. B.The two polygons are similar. Find y. Use the congruent angles to write the corresponding vertices in order. polygon ABCDE ~ polygon RSTUV Similarity proportion AB = 6, RS = 4, DE = 8, UV = y + 1 Cross Products Property Multiply. Subtract 6 from each side. Divide each side by 6 and simplify.

  14. Page 471 If two polygons are similar, their perimeters should have the same scale factor as the sides. Be sure to find the sum of all side lengths when finding the perimeter of the polygon. You may have to use other markings or geometric principles to find the length of unmarked sides!!!

  15. The scale factor ABCDE to RSTUV is or . Write a proportion to find the length of DC. 4 __ AE ___ 7 VU Since DC AB and AE  DE, the perimeter of ABCDE is 6 + 6 + 6 + 4 + 4 or 26. If ABCDE ~ RSTUV, find the scale factor of ABCDE to RSTUV and the perimeter of each polygon. Write a proportion. 4(10.5) = 7 ● DCCross Products Property 6 = DC Divide each side by 7.

  16. Use the perimeter of ABCDE and scale factor to write a proportion. Let x represent the perimeter of RSTUV. Theorem 7.1 Substitution 4x = (26)(7) Cross Products Property x = 45.5 Solve. Answer:The perimeter of ABCDE is 26 and the perimeter of RSTUV is 45.5.

  17. Map Reading The scale on a map relates the size of an object on the map to its actual size. Where do you find the scale on a map? Use the scale and algebra to find the distance between Mishawaka and Kokomo.

  18. 7-2 Assignment p. 473, 8-14 even, 18-24 even, 27-28

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