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Transcript
Warm-Ups • The number of students that participate in sports programs at Central High School is 520. The total number of students in the school is 1850. Find the athlete-to-student ratio to the nearest tenth. • In ∆EFG, the ratio of the measures of the angles is 5:12:13, and the perimeter is 90 centimeters. Find the measures of the angles. Happy Thursday! Today: Warm-Ups Similar Polygons Activity Similar Polygons Notes • CC.9-12.G.SRT.5- Use congruence and similarity criteria for triangles so solve problems and prove relationships in geometric figures. • • • • Use similarity statements. Find and use the scale factor. Use similar polygons. Find perimeters of similar figures. Activity • Get into groups that are no larger than four. • Cut out your triangles. • Sort your triangles into groups based on similar characteristics. • Stop here! We are going to share! Activity • What are similar triangles? • Group together similar triangles. • Label your triangles 1a, 1b, 1c, 2a, 2b, 2c and 3a, 3b, 3c. Group 1 should be acute triangles, group 2 should be right triangles and group 3 should be obtuse triangles. Letter a should go with your smallest triangle, b the middle triangle and, and c the largest triangle. • Match up each groups corresponding angles. Mark the angles. Use Similarity Statements • What did we say that similar polygons were? What criteria do they meet? • Two Polygons are similar if corresponding angles are congruent and corresponding side lengths are proportional. Example: Check! Finding the Scale Factor • If two polygons are similar then the ratio of the lengths of two corresponding sides is called the scale factor. • What was our scale factor in example 1? Example • Step 1: Identify pairs of congruent angles • Step 2: Show that the corresponding side lengths are proportional Using Similar Polygons • In the diagram, △ DEF ~ △MNP. Find the value of x. Solution Perimeters of Similar Polygons • If two polygons are similar then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.