Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Find the cross products, and 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

I can use ratios to determine if two figures are similar.

Vocabulary similar corresponding sides corresponding angles

Similar figures are figures that have the same shape but are not the same size. The symbol ~ means “is similar to.”

Corresponding angles of two or more similar polygons are in the same relative position. Corresponding sides of two or more similar polygons are in the same relative position. When naming similar figures, list the corresponding angles in the same order. For the triangles below, ∆ABC ~ ∆DEF. D E F A B C

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

A side of a figure can be named by its endpoints, with a bar above such as; Without the bar, the letters indicate the length of the side. Reading Math

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.

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.

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 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 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.

Tell whether the figures are similar. 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 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 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.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Tell whether the figures are similar. 1. Lesson Quiz: Part I Tell whether the figures are similar. 1. 59° 35° 86° similar

Tell whether the figures are similar. 2. Lesson Quiz: Part II Tell whether the figures are similar. 2. 119° 55° 107° 79° 80° 135° 38° not similar

Lesson Quiz for Student Response Systems 1. Which of the following triangles are similar? A. C. B. D.

Lesson Quiz for Student Response Systems 2. Which of the following figures are similar? A. B.