Similar Figures and Proportions 5-7 Similar Figures and Proportions Course 2 Warm Up Problem of the Day Lesson Presentation

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions Warm Up Find the cross products, then tell whether the ratios are equal. 16 6 , 40 15 1. 240 = 240; equal 3 8 18 46 , 2. 138 = 144; not equal 8 9 , 24 27 3. 216 = 216; equal 28 12 , 42 18 4. 504 = 504; equal

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions Problem of the Day Every 8th telephone pole along a road has a red band painted on it. Every 14th pole has an emergency call phone on it. What is the number of the first pole with both a red band and a call phone? 56

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions Learn to use ratios to determine if two figures are similar.

Insert Lesson Title Here Course 2 5-7 Similar Figures and Proportions Insert Lesson Title Here Vocabulary similar corresponding sides corresponding angles

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions Octahedral fluorite is a crystal found in nature. It grows in the shape of an octahedron, which is a solid figure with eight triangular faces. The triangles in different-sized fluorite crystals are similar figures. Similar figures have the same shape but not necessarily the same size.

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions When naming similar figures, list the letters of the corresponding vertices in the same order. In the previous table ∆ABC ~ ∆DEF. Writing Math

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles. 82◦ Corresponding angles D E F Corresponding sides A B C 55◦ 43◦

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions SIMILAR FIGURES Two figures are similar if The measures of their corresponding angles are equal. The ratios of the lengths of the corresponding sides are proportional.

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions A side of a figure can be named by its endpoints, with a bar above. AB Without the bar, the letters indicate the length of the side. Reading Math

Additional Example 1: Determining Whether Two Triangles Are Similar Course 2 5-7 Similar Figures and Proportions Additional Example 1: Determining Whether Two Triangles Are Similar Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E AB corresponds to DE. 16 in 10 in A C 28 in BC corresponds to EF. 4 in D 7 in 40 in F AC corresponds to DF. B AB DE = ? BC EF = ? AC DF Write ratios using the corresponding sides. 4 16 = ? 7 28 = ? 10 40 Substitute the length of the sides. 1 4 = ? 1 4 = ? 1 4 Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the triangles are similar.

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions Check It Out: Example 1 Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E AB corresponds to DE. 9 in 9 in A C 21 in BC corresponds to EF. 3 in D 7 in 27 in F AC corresponds to DF. B AB DE = ? BC EF = ? AC DF Write ratios using the corresponding sides. 3 9 = ? 7 21 = ? 9 27 Substitute the length of the sides. 1 3 = ? 1 3 = ? 1 3 Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the triangles are similar.

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions Additional Example 2: Determining Whether Two Four-Sided Figures are Similar Tell whether the figures are similar. The corresponding angles of the figures have equal measure. Write each set of corresponding sides as a ratio.

Additional Example 2 Continued Course 2 5-7 Similar Figures and Proportions Additional Example 2 Continued MN QR MN corresponds to QR. NO RS NO corresponds to RS. OP ST OP corresponds to ST. MP QT MP corresponds to QT.

Additional Example 2 Continued Course 2 5-7 Similar Figures and Proportions Additional Example 2 Continued Determine whether the ratios of the lengths of the corresponding sides are proportional. MN QR = ? NO RS OP ST MP QT Write ratios using corresponding sides. 6 9 = ? 8 12 4 10 15 Substitute the length of the sides. 2 3 = ? Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the figures are similar.

Similar Figures and Proportions Course 2 5-7 Similar Figures and Proportions Check It Out: Example 2 Tell whether the figures are similar. 100 m 80 m 60 m 47.5 m 80° 90° 125° 65° M P N O 400 m 320 m 190 m 240 m Q T R S The corresponding angles of the figures have equal measure. Write each set of corresponding sides as a ratio.

Check It Out: Example 2 Continued Course 2 5-7 Similar Figures and Proportions Check It Out: Example 2 Continued 100 m 80 m 60 m 47.5 m 80° 90° 125° 65° M P N O 400 m 320 m 190 m 240 m Q T R S MN QR MN corresponds to QR. NO RS NO corresponds to RS. OP ST OP corresponds to ST. MP QT MP corresponds to QT.

Check It Out: Example 2 Continued Course 2 5-7 Similar Figures and Proportions Check It Out: Example 2 Continued Determine whether the ratios of the lengths of the corresponding sides are proportional. 100 m 80 m 60 m 47.5 m 80° 90° 125° 65° M P N O 400 m 320 m 190 m 240 m Q T R S MN QR = ? NO RS OP ST MP QT Write ratios using corresponding sides. 60 240 = ? 80 320 47.5 190 100 400 Substitute the length of the sides. 1 4 = ? Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the figures are similar.

Similar Figures and Proportions Insert Lesson Title Here Course 2 5-7 Similar Figures and Proportions Insert Lesson Title Here Lesson Quiz: Part I Tell whether the figures are similar. 1. 59° 35° 86° similar

Similar Figures and Proportions Insert Lesson Title Here Course 2 5-7 Similar Figures and Proportions Insert Lesson Title Here Lesson Quiz: Part II Tell whether the figures are similar. 2. 119° 55° 107° 79° 80° 135° 38° not similar