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Geometry B Date: _____________ 7.1 Ratios in Similar Polygons Objective: To identify similar polygons and apply their properties to solve problems Definition: Similar Polygons: ___________________________________________________________ o Corresponding Angles are ______________________ o Corresponding Sides are _______________________ o The symbol for similarity is __________ Ex. 1: Describing Similar Polygons Identify the pairs of corresponding angles and sides in the similar triangles below. Angles: ____________ ____________ ____________ Sides: ____________ ____________ ____________ Similarity Statement: __________________________ Practice: Angles: _________ __________ ___________ Sides: __________ __________ __________ 0.5 Similarity Statement: __________________________ Similarity Ratio (or Scale Factor): _______________________________________________ Similarity Ratio of ΔABC to ΔDEF: ___________________________ Similarity Ratio of ΔDEF to ΔABC: ___________________________ Ex. 2: Writing Similarity Ratios Write the similarity ratio for the two sets of triangles from Example 1. Similarity Ratio of ΔABC to ΔJGH: ________ Similarity Ratio of ΔMNP to ΔTQR: ________ How to tell if two polygons are similar: Are all of the angles congruent? Are the sides proportional? Order sides from least to greatest and match corresponding sides together. Check to see if they all have the same similarity ratio. If you answered “yes” to both of those questions, the polygons are similar. Ex. 2: Identifying Similar Polygons Determine whether the two polygons are similar. If yes, write a similarity statement and the scale factor. a. ABCD and EFGH are both rectangles. b. Practice: Determine whether the two polygons are similar. If yes, write a similarity statement and the scale factor. Ex. 3: Finding Missing Sides of Similar Polygons The polygons below are similar. Use a proportion to find the missing value. a. b. Ex. 4: Similarity Application 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 HW: 7.1 Worksheet