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Similar Polygons

Solve each proportion. 1. ABC HIJ. Name three pairs of congruent sides. 2. = 3. = 4. = 5. =. 3 4. x 8. 2 x. 8 24. x 9. 1 3. 10 25. 2 x. Similar Polygons. Lesson 7-2. Check Skills You’ll Need. (For help, go to Lessons 4-1 and 7-1.).

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Similar Polygons

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  1. Solve each proportion. 1.ABC HIJ. Name three pairs of congruent sides. 2. = 3. = 4. = 5. = 34 x8 2x 8 24 x9 1 3 1025 2x Similar Polygons Lesson 7-2 Check Skills You’ll Need (For help, go to Lessons 4-1 and 7-1.) Check Skills You’ll Need 7-2

  2. 1. Choose pairs of letters in the same position on each part of the congruence statement ABC HIJ: AB HI, AC HJ, BC IJ 2. Multiply both sides of = by 8: x =  =  = 6 3. Simplify in = : = ; use the Cross Product Property: (1)x = (2)(3); simplify: x = 6 4. Multiply both sides of = by 9: x =  = = 3 5. Simplify in = : = ; use the Cross Product Property:(2)x = (5)(2); simplify: 2x = 10; divide by 2: x = 5 3 4 x 8 3 4 8 1 3 1 2 1 8 24 2 x 8 24 2 x 1 3 x 9 1 3 1 3 9 1 9 3 10 25 10 25 2 x 2 5 2 x Similar Polygons Lesson 7-2 Check Skills You’ll Need Solutions 7-2

  3. 1. A scale model of a boat is 9 in. long. The boat’s actual length is 60 ft. Find the ratio of the length of the scale model to the length of the boat. 2. Solve the proportion = . 3. A map uses the scale 1 cm = 20 mi. A county is 90 mi wide. How wide is the county on the map? If = , complete each of the following. 4. = 5. 7y = ? 6. = 10 8 15 x 1 2 4 cm x y 7 11 y x ? ? x + y y ? 11 Ratios and Proportions Lesson 7-1 Lesson Quiz 1 : 80 12 11 7 11x 18 7-2

  4. Similar Polygons Lesson 7-2 Notes Two figures that have the same shape but not necessarily the same size are similar (~). Two polygons are similar if (1) corresponding angles are congruent and (2) corresponding sides are proportional. The ratio of the lengths of corresponding sides is the similarity ratio. 7-2

  5. Similar Polygons Lesson 7-2 Notes A golden rectangle is a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle. In any golden rectangle, the length and width are in the golden ratio, which is about 1.618 : 1. 7-2

  6. BC YZ ? XZ = a.BY and mY = 78, so mB = 78 because congruent angles have the same measure. AC XZ BC YZ b.Because AC corresponds to XZ, . = Similar Polygons Lesson 7-2 Additional Examples Understanding Similarity ABC ~ XYZ Complete each statement. a.mB = ? b. Two polygons are similar if (1) corresponding angles are congruent and (2) corresponding sides are proportional. Quick Check 7-2

  7. Check that the corresponding sides are proportional. 1 2 AB JK 2 4 BC KL 1 2 CD LM 2 4 DA MJ = = = = Similar Polygons Lesson 7-2 Additional Examples Determining Similarity Determine whether the parallelograms are similar. Explain. Corresponding sides of the two parallelograms are proportional. Check that corresponding angles are congruent. B corresponds to K, but mB≠mK, so corresponding angles are not congruent. Although corresponding sides are proportional, the parallelograms are not similar because the corresponding angles are not congruent. Quick Check 7-2

  8. Because ABC ~ YXZ, you can write and solve a proportion. AC YZ BC XZ = Corresponding sides are proportional. x 40 12 30 = Substitute. 12 30 Solve for x. x =  40 Similar Polygons Lesson 7-2 Additional Examples Using Similar Figures If ABC ~ YXZ, find the value of x. x = 16 Quick Check 7-2

  9. Postcard width postcard length Painting width painting length Corresponding sides are proportional. = x 24 6 36 = Substitute. 6 36 Solve for x. x =  24 Similar Polygons Lesson 7-2 Additional Examples Real-World Connection A painting is 24 in. wide by 36 in. long. The length of a postcard reduction of the painting is 6 in. How wide is the postcard? The postcard and the painting are similar rectangles, so you can write a proportion. Let x represent the width of the postcard. x = 4 The postcard is 4 in. wide. Quick Check 7-2

  10. Let represent the longer side of the tabletop. 40 1.1618 1 Write a proportion using the Golden Ratio. = = 64.72 Cross-Product Property Similar Polygons Lesson 7-2 Additional Examples Real-World Connection The dimensions of a rectangular tabletop are in the Golden Ratio. The shorter side is 40 in. Find the longer side. The table is about 65 in. long. Quick Check 7-2

  11. Similar Polygons Lesson 7-2 Lesson Quiz Use the trapezoids below for Exercises 1–3. DFHN ~ BMLP. Complete each statement. 74 1.mH = ? 2. x = ? 3.mD = ? 49 99 4. A 4-in. by 6-in. drawing is enlarged to fit on a poster that measures 20 in. by 24 in. What are the dimensions of the largest drawing possible? 5. A rectangle with a perimeter 20 cm has a side 4 cm long. A rectangle with perimeter 40 cm has a side 8 cm long. Determine whether the rectangles are similar. If they are, give the similarity ratio. If they are not, explain. 6. The longer side of the golden rectangle is 20 ft. Find the length of the shorter side, rounded to the nearest tenth. 16 in. by 24 in. yes; 1 : 2 ≈ 12.4 ft 7-2

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