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SIMILAR FIGURES Objective: Learn to determine whether figures are similar, to use scale factors and to find missing dimensions in similar figure. SIMILAR FIGURES What are Similar Figure? Similar figure are figures that have the same shape but not necessarily the same size. The symbol “~” means “is similar to” These are B corresponding angles E A These are corresponding angles C D F CORRESPONDING ANGLES What are Corresponding Angles? Corresponding angles are matching angles of two or more similar figures, in the same position. These are corresponding sides B E A These are corresponding angles C F D CORRESPONDING SIDES What are Corresponding Sides? Corresponding sides are matching sides of two or more similar figures, in the same position. These are corresponding sides B E A These are corresponding angles C F D SIMILAR FIGURES Similar Figures Two figures are similar if: • The measures of their corresponding angles are equal • The ratios of the lengths of their corresponding sides are proportional The ratio formed by the corresponding sides is the scale factor TRY THIS!!! A picture 4 in. tall and 9 in. wide is to be scaled to 2.5 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? To find the scale factor, divide the known height of the scaled picture by the corresponding height of the original picture height of scaled pic 2.5 6.25 height of original pic 4 Then multiply the width of the original picture by the scale factor 6.25 9 5.625 The picture should be 5.625 in. wide. TRY THIS!!! A company’s logo is in the shape of an isosceles triangle with two sides that are 2.4 in. long and one side that is 1.8 in. long. On billboard, the triangle in the logo has two sides that each 8 ft. long. What is the length of the third side of the triangle on the billboard? 2.4in 1.8in 8 ft x ft Write the proportion 2.4in x ft 8 ft 1.8in 2.4 x 8 1.8 2.4 x 14.4 x6 Find the cross product in (ft) on both sides cancel Solve for x The third side of the triangle is 6 ft long REMEMBER! Remember! A C X B Z Y The following are matching, or corresponding: A and X AB and XY B and Y BC and YZ C and Z AC and XZ TRY THIS!!! Which rectangles are similar? Since the three figures are rectangles all the angles are right angles. A 3in 2in B 3in 4in C 6in Compare the ratios of corresponding sides to see if they are equal. length of rect. A 3 ?2 width of rect. A length of rect. B 4 3 width of rect. B 98 The ratios are not equal. Rectangle A is not similar to rectangle B length of rect. A 3?2 width of rect. A length of rect. C 6 4 width of rect. C 12 12 The ratios are equal. Rectangle A is similar to rectangle C or A~C 4in EXAMPLE 1: EXAMPLE 2: EXAMPLE 3: