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**5-5**Similar Figures and Proportions Course 2 Warm Up Problem of the Day Lesson Presentation**5-5**Similar Figures and Proportions 138 = 144; not equal Course 2 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. 8 9 24 27 , 3. 216 = 216; equal 28 12 42 18 , 4. 504 = 504; equal**5-5**Similar Figures and Proportions Course 2 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. If pole 1 has neither, what is the number of the first pole with both a red band and a call phone? pole 56**5-5**Similar Figures and Proportions Course 2 Learn to use ratios to determine if two figures are similar.**5-5**Similar Figures and Proportions Course 2 Insert Lesson Title Here Vocabulary similar corresponding sides corresponding angles**5-5**Similar Figures and Proportions Course 2 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. Similarfigures have the same shape but not necessarily the same size.**5-5**Similar Figures and Proportions Corresponding sides E B D F A C Corresponding angles Course 2 Matching sides of two or more polygons are called correspondingsides, and matching angles are called corresponding angles.**5-5**Similar Figures and Proportions Course 2 To find out if triangles are similar, determine whether the ratios of the lengths of their corresponding sides are proportional. If the ratios are proportional, then the corresponding angles must have equal measures.**5-5**Similar Figures and Proportions Reading Math 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. Course 2**5-5**Similar Figures and Proportions AB corresponds to DE. AC corresponds to DF. BC corresponds to EF. ? ? ? ? ? ? = = = = = = Course 2 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 16 in 10 in A C 28 in D 4 in 7 in 40 in F B AB DE BC EF AC DF Write ratios using the corresponding sides. 4 16 10 40 7 28 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.**5-5**Similar Figures and Proportions AB corresponds to DE. AC corresponds to DF. BC corresponds to EF. ? ? ? ? ? ? = = = = = = Course 2 Try This: Example 1 Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E 9 in 9 in A C 21 in D 3 in 7 in 27 in F B AB DE BC EF AC DF Write ratios using the corresponding sides. 3 9 9 27 7 21 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.**5-5**Similar Figures and Proportions Course 2 In figures with four or more sides, it is possible for the corresponding side lengths to be proportional and the figures to have different shapes. To find out if these figures are similar, first check that their corresponding angles have equal measures. 8 m 10 m 4 m 4 m 5 m 5 m 8 m 10 m 10 m 8 m 5 m 4 m =**5-5**Similar Figures and Proportions Course 2 Additional Example 2: Determining Whether Two Four-Sided Figures are Similar Use the properties of similarity to determine whether the figures are similar. The corresponding angles of the figures have equal measure. Write each set of corresponding sides as a ratio.**5-5**Similar Figures and Proportions MN corresponds to QR. NO corresponds to RS. OP corresponds to ST. MP corresponds to QT. Course 2 Additional Example 2 Continued MN QR NO RS OP ST MP QT**5-5**Similar Figures and Proportions ? ? ? ? ? ? OP ST MN QR NO RS MP QT = = = = = = 8 12 6 9 4 6 10 15 ? ? ? 2 3 2 3 2 3 2 3 = = = Course 2 Additional Example 2 Continued Determine whether the ratios of the lengths of the corresponding sides are proportional. Write ratios using corresponding sides. Substitute the length of the sides. Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the figures are similar.**5-5**Similar Figures and Proportions M P 100 m 80° 65° 60 m 47.5 m 125° 90° O 80 m N Q T 400 m 80° 65° 240 m 190 m 125° 90° S R 320 m Course 2 Try This: Example 2 Use the properties of similarity to determine whether the figures are similar. The corresponding angles of the figures have equal measure. Write each set of corresponding sides as a ratio.**5-5**Similar Figures and Proportions M P 100 m 80° 65° MN corresponds to QR. 60 m 47.5 m 125° 90° O NO corresponds to RS. 80 m N Q T 400 m OP corresponds to ST. 80° 65° MP corresponds to QT. 240 m 190 m 125° 90° S R 320 m Course 2 Try This: Example 2 Continued MN QR NO RS OP ST MP QT**5-5**Similar Figures and Proportions M P 100 m 80° 65° ? ? ? ? ? ? OP ST MN QR NO RS MP QT 60 m = = = 47.5 m = = = 125° 90° O 80 m N 80 320 60 240 47.5 190 100 400 Q T 400 m 80° 65° ? ? ? 1 4 1 4 1 4 1 4 = = = 240 m 190 m 125° 90° S R 320 m Course 2 Try This: Example 2 Continued Determine whether the ratios of the lengths of the corresponding sides are proportional. Write ratios using corresponding sides. Substitute the length of the sides. Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the figures are similar.**5-5**Similar Figures and Proportions NO corresponds to QR; PN corresponds to SQ; similar PO corresponds to SR; Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 1. Identify the corresponding sides in the pair of triangles, and use ratios to determine whether the triangles are similar.**5-5**Similar Figures and Proportions Course 2 Insert Lesson Title Here Lesson Quiz 2. Use properties of similarity to determine whether the figures are similar. not similar