Course Similar Figures Warm Up Solve each proportion. b = y5y5 = p9p9 = m = 4. b = 10y = 8 p = 3 m = 52

Course Similar Figures Problem of the Day A rectangle that is 10 in. wide and 8 in. long is the same shape as one that is 8 in. wide and x in. long. What is the length of the smaller rectangle? 6.4 in.

Course Similar Figures Learn to determine whether figures are similar, to use scale factors, and to find missing dimensions in similar figures. TB P

Course Similar Figures Vocabulary similar congruent angles scale factor

Course Similar Figures Similar figures have the same shape, but not necessarily the same size. Two triangles are similar if the ratios of the lengths of corresponding sides are equivalent and the corresponding angles have equal measures. Angles that have equal measures are called congruent angles. 43°

Course Similar Figures Additional Example 1: Identifying Similar Figures Which rectangles are similar? Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

Course Similar Figures Additional Example 1 Continued 50  48 The ratios are equal. Rectangle J is similar to rectangle K. The notation J ~ K shows similarity. The ratios are not equal. Rectangle J is not similar to rectangle L. Therefore, rectangle K is not similar to rectangle L. 20 = 20 length of rectangle J length of rectangle K width of rectangle J width of rectangle K ? = length of rectangle J length of rectangle L width of rectangle J width of rectangle L ? = Compare the ratios of corresponding sides to see if they are equal.

Course Similar Figures The ratio formed by the corresponding sides is the scale factor.

Course Similar Figures Additional Example 2A: Using 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? Divide the height of the scaled picture by the corresponding height of the original picture = Multiply the width of the original picture by the scale factor The picture should be 2.1 in. wide. Simplify.

Course Similar Figures Additional Example 2B: Using Scale Factors to Find Missing Dimensions A toy replica of a tree is 9 inches tall. What is the length of the tree branch, if a 6 ft tall tree has a branch that is 60 in. long? Divide the height of the replica tree by the height of the 6 ft tree in inches, to find the scale factor = Multiply the length of the original tree branch by the scale factor The toy replica tree branch should be 7.5 in long. Simplify.

Course Similar Figures Additional Example 3: Using Equivalent Ratios to Find Missing Dimensions A T-shirt design includes an isosceles triangle with side lengths 4.5 in, 4.5 in., and 6 in. An advertisement shows an enlarged version of the triangle with two sides that are each 3 ft. long. What is the length of the third side of the triangle in the advertisement? Set up a proportion. 6 in. x ft 4.5 in. 3 ft = 4.5 in. x ft = 3 ft 6 in. Find the cross products. 4.5 in. x ft = 3 ft 6 in. Divide out the units.

Course Similar Figures Draw a diagram to help you visualize the problems Helpful Hint

Course Similar Figures 4.5x = x = 18 x = = Cancel the units. Multiply. Solve for x. Additional Example 3 Continued The third side of the triangle is 4 ft long.

Course Similar Figures Lesson Quiz Use the properties of similar figures to answer each question. 1. A rectangular house is 32 ft wide and 68 ft long. On a blueprint, the width is 8 in. Find the length on the blueprint. 2. Karen enlarged a 3 in. wide by 5 in. tall photo into a poster. If the poster is 2.25 ft wide, how tall is it? 3. Which rectangles are similar? 17 in ft A and B are similar.