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- 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. 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. 7-2 Ratios in Similar Polygons Objectives Identify similar polygons. Apply properties of similar polygons to solve problems.Holt McDougal Geometry
- 4. 7-2 Ratios in Similar Polygons Vocabulary similar similar polygons similarity ratioHolt McDougal Geometry
- 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. Proving Similar Triangles• Are the triangles similar?15 12 16 20 18 24
- 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. Are these similar? 6 21 185
- 9. Scale FactorThe ratio of the lengths of two corresponding sides of similar polygons.
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 7-2 Ratios in Similar Polygons Helpful Hint When you work with proportions, be sure the ratios compare corresponding measures.Holt McDougal Geometry
- 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. 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. 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. 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. Perimeter of similar polygons• The ratio of the perimeters of two similar polygons is the same as the ratio of the corresponding sides
- 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. 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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