Presentation on theme: " Similar figures have the same shape, but not necessarily the same size."— Presentation transcript:
Similar figures have the same shape, but not necessarily the same size.
14 m 7m 60° The ratio formed by the sides is the scale factor: 14m = 2m 7m 1m
1. Set up a proportion: Large ∆ to Small ∆ 2. Large ∆ 15 = 12 Small ∆ 5 x 3. Cross multiply and solve x = x = 4 The missing length of ∆NMP is 4 cm. P N M C B A 12 cm 5 cm 15 cm X ∆ABC is similar to ∆NMP. Find the length of X.
Trapezoid DEFG is similar to trapezoid HJKL. Find the length of side LK. L K J H G F E D 8 cm 10 cm 15 cm 1. Set up a proportion: Small trapezoid to Large trapezoid 2. Small 8 = 10 Large 15 x 3. Cross multiply and solve. 4. 8x = x = The length of LK is cm.
V U T SR FE D C B A W Polygon ABCDEF is similar to polygon RSTUVW. Find the lengths of RS and WV. 20 m 8 m 6 m 12 m 1. Set up a proportion: Large polygon to Small polygon 2. Large 20 = 6 Small 8 x (RS) 3. Cross multiply and solve x = x = The length of RS is 2.4 m. 1. Set up a proportion: Large polygon to Small polygon 2. Large 20 = 12 Small 8 x (WV) 3. Cross multiply and solve x = x = The length of WV is 4.8 m.
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. Step 2: Set up a proportion. Large 10 = 14 Small 1.5 x 14(1.5) = 10x 21 = 10x The picture should be 2.1 in. wide. ? in. 1.5 in. 14 in. 10 in.
Set up a proportion.24 ft x in. 18 ft 4 in. = 18 ft x in. = 24 ft 4 in.Find the cross products. 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? 18 ft 24ft 18x = 96 x = Multiply Solve for x. The third side of the triangle is about 5.3 in. long.
A 8 ft 4 ft B6 ft 3 ft C 5 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.
A 8 ft 4 ft B6 ft 3 ft C 5 ft 2 ft The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity. 24 = 24 length of rectangle A length of rectangle B width of rectangle A width of rectangle B ? =
A 8 ft 4 ft B6 ft 3 ft C 5 ft 2 ft The ratios are NOT equal. Rectangle A is NOT similar to rectangle C. 16 20 length of rectangle A length of rectangle C width of rectangle A width of rectangle C ? =