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Similar Polygons What are similar polygons? Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional. Congruent Figures • In order to be congruent, two figures must be the same size and same shape. • ~ = Similar Figures • Similar figures must be the same shape, but their sizes may be different. • ~ Angles and Sides in Similar Polygons Angles Sides ∠A ≅ ∠ E AB ~ EF ∠B ≅ ∠ F AC ~ EG ∠C ≅ ∠ G BC ~ FG A ΔABC ~ ΔEFG E B C F G You can find the missing length of a side in a pair of similar figures, by using ΔRST ~ ΔUVW proportions R U x ft. 6 ft. S T 35 ft. 6 x 7 ft. 7 = W V 35 x = 30 feet Solve for x. 40 in. 30 in.. 12 in. x in. x 12 30 = 40 x = 9 inches Solve for x. Round to the nearest tenth. 12 in. 4 in. 20 in. x in.. 4 12 x = 20 x = 6.7 inches Solve for x. x 25 m. 14 m. 7 m. 7 14 = 25 x x = 50 meters 17 in. Solve for x. Round to the nearest tenth. x 35 in. 15 in. 15 = 35 x 17 x = 7.3 inches Determine the missing sides of the triangle 39 in ? in 33 in 24 in ? in 8 in Determine the length of the missing side • Two rectangles are similar. The first is 4 in. wide and 15 in. long. The second is 9 in. wide. Find the length of the second rectangle. Determine the length of the missing side • Two rectangles are similar. One is 5 cm by 12 cm. The longer side of the second rectangle is 8 cm greater than twice the shorter side. Find its length and width. Similar Figures Which of the following is not a characteristic of similar figures? A. Proportional sides B. Equal angle measurements C. Same shape D. Congruent side lengths Similar Figures • Are the figures below similar? Explain. Similar Figures • Are the figures below similar? Explain.