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Concept

Concept. Use a Similarity Statement. If Δ ABC ~ Δ RST , list all pairs of congruent angles and write a proportion that relates the corresponding sides. Example 1. Use a Similarity Statement. Use the similarity statement. Δ A B C ~ Δ R S T. Answer:.

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Concept

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  1. Concept

  2. Use a Similarity Statement If ΔABC ~ ΔRST, list all pairs of congruent angles and write a proportion that relates the corresponding sides. Example 1

  3. Use a Similarity Statement Use the similarity statement. ΔABC ~ ΔRST Answer: Congruent Angles: A R, B S,C T Example 1

  4. A.HGK  QPR B. C.K  R D.GHK  QPR If ΔGHK ~ ΔPQR, determine which of the following similarity statements is not true. Example 1

  5. Identify Similar Polygons A. MENUSTan is designing a new menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning. Original Menu: New Menu: Example 2

  6. Identify Similar Polygons Step 1 Compare corresponding angles. Since all angles of a rectangle are right angles and right angles are congruent, corresponding angles are congruent. Step 2 Compare corresponding sides. Answer:Since corresponding sides are not proportional, ABCD is not similar to FGHK. So, the menus are not similar. Example 2

  7. Identify Similar Polygons B. MENUSTan is designing a new menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning. Original Menu: New Menu: Example 2

  8. Identify Similar Polygons Step 1 Compare corresponding angles. Since all angles of a rectangle are right angles and right angles are congruent, corresponding angles are congruent. Step 2 Compare corresponding sides. Example 2

  9. Answer:Since corresponding sides are proportional, ABCD ~ RSTU. So, the menus are similar with a scale factor of . 4 __ 5 Identify Similar Polygons Example 2

  10. Use Similar Figures to Find Missing Measures A.The two polygons are similar. Find x. Use the congruent angles to write the corresponding vertices in order. polygon ABCDE ~ polygon RSTUV Example 3

  11. 9 __ 2 Answer: x = Use Similar Figures to Find Missing Measures Write a proportion to find x. Similarity proportion Cross Products Property Multiply. Divide each side by 4. Simplify. Example 3

  12. Use Similar Figures to Find Missing Measures B.The two polygons are similar. Find y. Use the congruent angles to write the corresponding vertices in order. polygon ABCDE ~ polygon RSTUV Example 3

  13. 13 __ 3 Answer: y = Use Similar Figures to Find Missing Measures 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. Example 3

  14. Concept

  15. Use a Scale Factor to Find Perimeter If ABCDE ~ RSTUV, find the scale factor of ABCDE to RSTUV and the perimeter of each polygon. Example 4

  16. 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. Use a Scale Factor to Find Perimeter Write a proportion. 4(10.5) = 7 ● DC Cross Products Property 6 = DC Divide each side by 7. Example 4

  17. Use a Scale Factor to Find Perimeter 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. Example 4

  18. Use a Scale Factor to Find Perimeter Answer:The perimeter of ABCDE is 26 and the perimeter of RSTUV is 45.5. Example 4

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