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Chapter 7 7-1 ratios in similar polygons

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Objectives Identify similar polygons. Apply properties of similar polygons to solve problems.

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Similar figures What is similar? Figures that are similar (~) have the same shape but not necessarily the same size.

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Similar polygons Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.

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Example 1: Describing Similar Polygons Identify the pairs of congruent angles and corresponding sides. N Q and P R. By the Third Angles Theorem, M T.

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Check it out! Identify the pairs of congruent angles and corresponding sides. B G and C H. By the Third Angles Theorem, A J.

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Similarity ratio What is a similarity ratio? 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 3/6, or 1/2. The similarity ratio of ∆DEF to ∆ABC is 6/3, or 2.

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Example 2A: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. rectangles ABCD and EFGH

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Solution Step 1 Identify pairs of congruent angles. A E, B F, C G, and D H. All s of a rect. are rt. s and are . Step 2 Compare corresponding sides. Thus the similarity ratio is 3/2, and rect. ABCD ~ rect. EFGH.

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Example 2B: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. ∆ ABCD and ∆ EFGH

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Solution Step 1 Identify pairs of congruent angles. P R and S W 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.

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Check it out! Determine if ∆ JLM ~ ∆ NPS. If so, write the similarity ratio and a similarity statement.

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Example 3: Hobby Application Find the length of the model to the nearest tenth of a centimeter.

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Solution 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.

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Solution 5(6.3) = x(1.8) 31.5 = 1.8x The length of the model is 17.5 centimeters.

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Check it out!! 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.

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Student Guided Practice Do problems 2-6 in your book page 469

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Homework! Do problems 7-11 in your book page 470.

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Closure Today we saw about similarity in polygons Next class we are going to see similarity and transformations

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