2 SimilarSimilar figures have the same shape, but not necessarily the same size.
3 Similar Polygons The ratio formed by the sides is the scale factor: 14m = 2m 7m m7m60°60°
4 Use proportions to find the length of the missing side of a similar polygon. XNM5 cm12 cm15 cmP∆ABC is similar to ∆NMP.Find the length of X.BCSet up a proportion: Large ∆ to Small ∆Large ∆ = 12 Small ∆ xCross multiply and solve.15x = 60x = The missing length of ∆NMP is 4 cm.
5 Use proportions to find the length of the missing side of a similar polygon. JTrapezoid DEFG is similar to trapezoid HJKL.Find the length of side LK.15 cmDE8 cmGLFK10 cmSet up a proportion: Small trapezoid to Large trapezoidSmall = 10 Large xCross multiply and solve.8x = 150x = The length of LK is cm.
6 Use proportions to find the length of the missing side of a similar polygon. BRSPolygon ABCDEF is similar to polygon RSTUVW.Find the lengths of RS and WV.8 m20 mTUCDWVFE12 mSet up a proportion: Large polygon to Small polygonLarge = 12 Small x (WV)Cross multiply and solve.20x = 96x = 4.8The length of WV is 4.8 m.Set up a proportion: Large polygon to Small polygonLarge = 6 Small x (RS)Cross multiply and solve.20x = 48x = 2.4The length of RS is 2.4 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 = 14 Small x? in.14 in.14(1.5) = 10x21 = 10xThe picture should be 2.1 in. wide.
8 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?24ftSet up a proportion.24 ftx in.18 ft4 in.=18ft18 ft18 ft • x in. = 24 ft • 4 in.Find the cross products.18x = 96Multiplyx = 5.39618Solve for x.The third side of the triangle is about 5.3 in. long.
9 Which rectangles are similar? 8 ftA6 ftBC5 ft4 ft3 ft2 ftSince 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 Which rectangles are similar? 8 ftA6 ftBC5 ft3 ft2 ft4 ftlength of rectangle Alength of rectangle Bwidth of rectangle Awidth of rectangle B8643?=24 = 24The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity.
11 Which rectangles are similar? 8 ftA6 ftBC5 ft3 ft2 ft4 ftlength of rectangle Alength of rectangle Cwidth of rectangle Awidth of rectangle C8542?=16 20The ratios are NOT equal. Rectangle A is NOT similar to rectangle C.