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Advanced Geometry Similarity Lesson 2 Proportions & Similarity Ratio a b The ratio of a to b can be expressed as , where b is not zero. FORMS: 1 to 2 1: 2 1 2 All ratios must be in simplest form. 24 3 8 1 32 : 6 16 : 3 A ratio in which the denominator is 1 is called a unit ratio. EXAMPLE: The number of students that participate in sports programs at Central High School is 550. The total number of students in the school is 1850. Find the athlete to non-athlete ratio. 4 x 5 26 3 6 x 2 3x 5 1 5 x3 An extended ratio is a ratio used to compare three or more numbers. Extended ratios are written using colons. EXAMPLE: In a triangle, the ratio of the measures of three angles is 1 1 1 : : . Find the measures of the angles of the triangle. 3 4 6 Example: The ratios of the sides of three polygons are given. Make a conjecture about the type of each polygon described. 2:2:3 3: 3: 3: 3 Isosceles triangle Rhombus 4:5:4:5 Similar Polygons In order for two polygons to be similar, all of their corresponding angles must be congruent and all of the corresponding sides must form a proportion. A B D F C E Similarity Statement: A E B F C D AB BC AC EF FD ED EXAMPLES: Determine whether each pair of figures is similar. Justify your answer. No; the corresponding angles are not congruent. EXAMPLE: An architect prepared a 12-inch model of a skyscraper to look like an actual 1100-foot building. What is the scale factor of the model compared to the actual building? EXAMPLE: Each pair of polygons is similar. Write a similarity statement, find x, y, ED, and the scale factor.