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Similar Figures

Similar Figures. Similar. Similar figures have the same shape, but not necessarily the same size. . Similar Polygons. 14 m. The ratio formed by the sides is the scale factor : 14m = 2m 7m 1m. 7m. 60°. 60°.

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Similar Figures

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  1. Similar Figures

  2. Similar • Similar figures have the same shape, but not necessarily the same size.

  3. Similar Polygons 14 m The ratio formed by the sides is the scale factor: 14m = 2m7m 1m 7m 60° 60°

  4. Use proportions to find the length of the missing side of a similar polygon. A • Set up a proportion: Large ∆ to Small ∆ • Large ∆15 = 12Small ∆ 5 x • Cross multiply and solve. • 15x = 60 • x = 4 The missing length of ∆NMP is 4 cm. X M N 5 cm 12 cm P 15 cm ∆ABC is similar to ∆NMP. Find the length of X. C B

  5. Use proportions to find the length of the missing side of a similar polygon. J H Trapezoid DEFG is similar to trapezoid HJKL. Find the length of side LK. • Set up a proportion: Small trapezoid to Large trapezoid • Small 8 = 10Large 15 x • Cross multiply and solve. • 8x = 150 • x = 18.75 The length of LK is 18.75 cm. 15 cm E D 8 cm L K G F 10 cm

  6. Use proportions to find the length of the missing side of a similar polygon. 6 m B A R S • Set up a proportion: Large polygon to Small polygon • Large 20 = 6Small 8 x (RS) • Cross multiply and solve. • 20x = 48 • x = 2.4 • The length of RS is 2.4 m. Polygon ABCDEF is similar to polygon RSTUVW. Find the lengths of RS and WV. 8 m 20 m T U C D W V F E 12 m • Set up a proportion: Large polygon to Small polygon • Large 20 = 12Small 8 x (WV) • Cross multiply and solve. • 20x = 96 • x = 4.8 • The length of WV is 4.8 m.

  7. Use Scale Factors to Find Missing Dimensions A picture 10 in. tall and 14 in. wide is to be scaled to 1.5 in. tall to be displayed on a Web page. How wide should the picture be on the Web page for the two pictures to be similar? Step 1: Draw & Label a picture. 1.5 in. 10 in. Step 2: Set up a proportion. Large 10= 14Small 1.5x ? in. 14 in. 14(1.5) = 10x 21 = 10x The picture should be 2.1 in. wide.

  8. 96 18 x =  5.3 18 ft 4 in. 24 ft x in. = Use Scale Factors to Find Missing Dimensions A flag in the shape of an isosceles triangle with side lengths 18 ft, 18 ft, and 24 ft is hanging on a pole outside a campground. A camp t-shirt shows a smaller version of the triangle with two sides that are each 4 in. long. What is the length of the third side of the triangle on the t-shirt? 24ft Set up a proportion. 18ft 18 ft 18 ft • x in. = 24 ft • 4 in. Find the cross products. 18x = 96 Multiply Solve for x. The third side of the triangle is about 5.3 in. long.

  9. Which rectangles are similar? 8 ft A 6 ft B C 5 ft 4 ft 3 ft 2 ft Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent. Compare the ratios of corresponding sides to see if they are equal.

  10. 4 3 length of rectangle A length of rectangle B 8 6 width of rectangle A width of rectangle B ? = Which rectangles are similar? 8 ft A 6 ft B C 5 ft 3 ft 2 ft 4 ft 24 = 24 The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity.

  11. 4 2 length of rectangle A length of rectangle C 8 5 width of rectangle A width of rectangle C ? = Which rectangles are similar? 8 ft A 6 ft B C 5 ft 3 ft 2 ft 4 ft 16  20 The ratios are NOT equal. Rectangle Ais NOTsimilar to rectangle C.

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