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Name______________________________________________ Class___________________ Congruent vs. Similar Polygons: Day 1 Congruent polygons: Symbol for congruent: Congruent polygons ∆ABC ∆DEF “Hash” marks show: “Hoops” show” Angles - Corresponding angles are congruent: A , B , and C Sides - Corresponding sides are congruent: EXAMPLE 1: Finding Measures of Congruent Polygons Given that ABCD WXYZ, mark the corresponding angles and sides. Then find the measurement of side XY. What is the measurement of XY? NOW YOU TRY IT! 1) Given that ∆ABC ∆LMN, mark the corresponding angles and sides. Then find the unknown angle measurements. Similar polygons: Symbol for similar: Similar Polygons ∆LMN ~ ∆PQR Angles: Corresponding angles are congruent: L , M , and N Sides: Ratios of corresponding sides are equal: EXAMPLE 2: Finding the Ratio of Lengths Given that ∆ABC ~ ∆DEF, mark the congruent angle and find the ratio of the lengths of the corresponding sides of ∆ABC to ∆DEF. Lengths of corresponding sides written as a ratio Simplify (if needed) NOW YOU TRY IT! 2) Given that XYZ ~ EFG, mark the congruent angles and find the ratio of the lengths of the corresponding sides. Lengths of corresponding sides written as a ratio Simplify (if needed) EXAMPLE 3: Checking for Similarity A photograph of a rug in a catalog is 10 centimeters long and 7 centimeters wide. The actual rug is 171 centimeters long and 92 centimeters wide. Are the photograph of the rug and the actual rug similar figures? (Draw a picture to help you out) NOW YOU TRY IT! 3) A landscape architect is planning a memorial 18 feet long and 15 feet wide. A rectangular blueprint of the garden has a length of 12 inches long and 10 inches wide. Are the garden and the blueprint similar figures?