Similar triangles day2

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Similar triangles day2

  1. 1. 7-2 Ratios in Similar Polygons HW On The Corner of Your Desk! Drill #3.12 2/20/13 1. If ∆QRS ∆ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Q Z; R Y; S X; QR ZY; RS YX; QS ZX Solve each proportion. 2. 3. x=9 x = 18Holt McDougal Geometry
  2. 2. 7-2 Ratios in Similar Polygons Lesson Review 1. The ratio of the angle measures in a triangle is 1:5:6. What is the measure of each angle? 15°, 75°, 90° Solve each proportion. 2. 3 3. 7 or –7 4. Given that 14a = 35b, find the ratio of a to b in simplest form. 5. An apartment building is 90 ft tall and 55 ft wide. If a scale model of this building is 11 in. wide, how tall is the scale model of the building? 18 in.Holt McDougal Geometry
  3. 3. 7-2 Ratios in Similar Polygons Objectives Identify similar polygons. Apply properties of similar polygons to solve problems.Holt McDougal Geometry
  4. 4. 7-2 Ratios in Similar Polygons Vocabulary similar similar polygons similarity ratioHolt McDougal Geometry
  5. 5. 7-2 Ratios in Similar Polygons Figures that are similar (~) have the same shape but not necessarily the same size.Holt McDougal Geometry
  6. 6. Proving Similar Triangles• Are the triangles similar?15 12 16 20 18 24
  7. 7. 7-2 Ratios in Similar Polygons Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.Holt McDougal Geometry
  8. 8. Are these similar? 6 21 185
  9. 9. Scale FactorThe ratio of the lengths of two corresponding sides of similar polygons.
  10. 10. 7-2 Ratios in Similar Polygons Example 1: Describing Similar Polygons Identify the pairs of congruent angles and 0.5 corresponding sides. N Q and P R. By the Third Angles Theorem, M T.Holt McDougal Geometry
  11. 11. 7-2 Ratios in Similar Polygons Check It Out! Example 1 Identify the pairs of congruent angles and corresponding sides. B G and C H. By the Third Angles Theorem, A J.Holt McDougal Geometry
  12. 12. 7-2 Ratios in Similar Polygons A similarity ratio is the ratio of the lengths of the corresponding sides of two similar polygons. The similarity ratio of ∆ABC to ∆DEF is , or . The similarity ratio of ∆DEF to ∆ABC is , or 2.Holt McDougal Geometry
  13. 13. 7-2 Ratios in Similar Polygons Writing Math Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.Holt McDougal Geometry
  14. 14. 7-2 Ratios in Similar Polygons Example 2A: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. rectangles ABCD and EFGHHolt McDougal Geometry
  15. 15. 7-2 Ratios in Similar Polygons Example 2A Continued Step 1 Identify pairs of congruent angles. A E, B F, All s of a rect. are rt. s C G, and D H. and are . Step 2 Compare corresponding sides.Thus the similarity ratio is , and rect. ABCD ~ rect. EFGH. Holt McDougal Geometry
  16. 16. 7-2 Ratios in Similar Polygons Example 2B: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. ∆ABCD and ∆EFGHHolt McDougal Geometry
  17. 17. 7-2 Ratios in Similar Polygons Example 2B Continued Step 1 Identify pairs of congruent angles. P R and S W isos. ∆ Step 2 Compare corresponding angles. m W = m S = 62° m T = 180° – 2(62°) = 56° Since no pairs of angles are congruent, the triangles are not similar.Holt McDougal Geometry
  18. 18. 7-2 Ratios in Similar Polygons Check It Out! Example 2 Determine if ∆JLM ~ ∆NPS. If so, write the similarity ratio and a similarity statement. Step 1 Identify pairs of congruent angles. N M, L P, S JHolt McDougal Geometry
  19. 19. 7-2 Ratios in Similar Polygons Check It Out! Example 2 Continued Step 2 Compare corresponding sides. Thus the similarity ratio is , and ∆LMJ ~ ∆PNS.Holt McDougal Geometry
  20. 20. 7-2 Ratios in Similar Polygons Helpful Hint When you work with proportions, be sure the ratios compare corresponding measures.Holt McDougal Geometry
  21. 21. 7-2 Ratios in Similar Polygons Example 3: Hobby Application Find the length of the model to the nearest tenth of a centimeter. Let x be the length of the model in centimeters. The rectangular model of the racing car is similar to the rectangular racing car, so the corresponding lengths are proportional.Holt McDougal Geometry
  22. 22. 7-2 Ratios in Similar Polygons Example 3 Continued 5(6.3) = x(1.8) Cross Products Prop. 31.5 = 1.8x Simplify. 17.5 = x Divide both sides by 1.8. The length of the model is 17.5 centimeters.Holt McDougal Geometry
  23. 23. 7-2 Ratios in Similar Polygons Check It Out! Example 3 A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch.Holt McDougal Geometry
  24. 24. 7-2 Ratios in Similar Polygons Check It Out! Example 3 Continued 1.25(36.25) = x(9) Cross Products Prop. 45.3 = 9x Simplify. 5 x Divide both sides by 9. The length of the model is approximately 5 inches.Holt McDougal Geometry
  25. 25. Perimeter of similar polygons• The ratio of the perimeters of two similar polygons is the same as the ratio of the corresponding sides
  26. 26. 7-2 Ratios in Similar Polygons Lesson Quiz: Part I 1. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. no 2. The ratio of a model sailboat’s dimensions to the actual boat’s dimensions is . If the length of the model is 10 inches, what is the length of the actual sailboat in feet? 25 ftHolt McDougal Geometry
  27. 27. 7-2 Ratios in Similar Polygons Lesson Quiz: Part II 3. Tell whether the following statement is sometimes, always, or never true. Two equilateral triangles are similar. AlwaysHolt McDougal Geometry

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