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Warm-up . You are building a scale model of your uncle’s fishing boat. The boat is 62 ft long and 23 ft wide. The model will be 14 in. long. How wide should it be? Find the geometric mean of 20 and 24.
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Warm-up • You are building a scale model of your uncle’s fishing boat. The boat is 62 ft long and 23 ft wide. The model will be 14 in. long. How wide should it be? • Find the geometric mean of 20 and 24. Geometric mean of two positive numbers a and b is the positive number x such that a b
Similar Polygons Objective: Identify similar polygons
Similar polygons: corresponding angles are congruent and the lengths of the corresponding sides are proportional. • KLMN ~ PQRS P K L Q N S M R
Theorem 8.1 • If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. If KLMN~PQRS, then P K L Q N S M R
YOUR TURN! • Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of congruent angles and write the ratios of the corresponding sides in a statement of proportionality. • You have a photo 4 in. wide by 6 in. long that you want to reduce to fit in a frame that is 1.5 in. wide. How long will the reduced photo be?
Verify that these two regular pentagons are similar. Then find the ratio of their perimeters. • These pentagons are similar because all the angles are congruent and all the corresponding sides are in the ratio 4:1;the perimeters have the ratio of4:1.It has a scale factor of 4 to 1 or 4/1. 1.5 m 6 m
Always, sometimes, or never similar. • Two isosceles triangles • Two regular polygons • Two isosceles trapezoids • Two rhombuses • Two squares • An isosceles and a scalene triangle • Two equilateral triangles • A right and an isosceles triangle sometimes sometimes sometimes sometimes always never always sometimes
abcd ~ gbef. Find the value of y. E C B 12 y G 15 F A D 24