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

Warm Up Find the cross products, then tell whether the ratios are equal. Course Similar Figures and Proportions , , , , = 240; equal 216 = 216; equal 504 = 504; equal 138 = 144; not equal

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 Course Similar Figures and Proportions

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

Vocabulary similar corresponding sides corresponding angles Insert Lesson Title Here Course Similar Figures and Proportions

Course 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.

Course Similar Figures and Proportions Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles. Corresponding angles A B C D E F Corresponding sides

Course Similar Figures and Proportions SIMILAR FIGURES If two figures are similar, then the measures of the corresponding angles are equal and the ratios of the lengths of the corresponding sides are proportional. 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.

Course 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

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

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

Course Similar Figures and Proportions 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. 10 m 5 m 8 m 4 m 10 m 8 m = 5 m 4 m

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

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

Determine whether the ratios of the lengths of the corresponding sides are proportional. Additional Example 2 Continued Course Similar Figures and Proportions 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. MN QR = ? NO RS = ? OP ST = ? MP QT 6 9 = ? 8 12 = ? 4 6 = ? = 2323 = 2323 = 2323 ? ? ?

Use the properties of similarity to determine whether the figures are similar. Try This: Example 2 Course Similar Figures and Proportions The corresponding angles of the figures have equal measure. 100 m 80 m 60 m 47.5 m 80° 90° 125° 65° MP N O 400 m 320 m 190 m240 m 80°65° 90° 125° QT R S Write each set of corresponding sides as a ratio.

Try This: Example 2 Continued Course Similar Figures and Proportions MN QR MN corresponds to QR. NO RS OP ST MP QT NO corresponds to RS. OP corresponds to ST. MP corresponds to QT. 100 m 80 m 60 m 47.5 m 80° 90° 125° 65° MP N O 400 m 320 m 190 m240 m 80°65° 90° 125° QT R S

Determine whether the ratios of the lengths of the corresponding sides are proportional. Try This: Example 2 Continued Course Similar Figures and Proportions 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. 100 m 80 m 60 m 47.5 m 80° 90° 125° 65° MP N O 400 m 320 m 190 m240 m 80°65° 90° 125° QT R S MN QR = ? NO RS = ? OP ST = ? MP QT = ? = ? = ? = 1414 = 1414 = 1414 ? ? ?

Lesson Quiz: Part 1 Insert Lesson Title Here Course Similar Figures and Proportions 1. Identify the corresponding sides in the pair of triangles, and use ratios to determine whether the triangles are similar. NO corresponds to QR; PN corresponds to SQ; similar PO corresponds to SR;

Lesson Quiz Insert Lesson Title Here Course Similar Figures and Proportions 2. Use properties of similarity to determine whether the figures are similar. not similar