Similar figures are figures that have the same shape but not necessarily the same size. The symbol ~ means “is similar to.” 1

For the triangles below, ∆ABC ~ ∆DEF. Corresponding angles Corresponding sides For the triangles below, ∆ABC ~ ∆DEF. D E F A B C 2

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 3

Additional Example 1: Determining Whether Two Triangles Are Similar Tell whether the triangles are similar. AB corresponds to BC corresponds to AC corresponds to AB DE = ? BC EF = ? AC DF Write ratios using the corresponding sides. Substitute the length of the sides. Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the triangles are similar. 4

Tell whether the triangles are similar. Example 1 Tell whether the triangles are similar. E 9 in. A C 9 in. 21 in. 3 in. 7 in. D B 27 in. F 5

Tell whether the figures are similar. Example 2: Tell whether the figures are similar. The corresponding angles of the figures have equal measure. Write each set of corresponding sides as a ratio. 6

Tell whether the figures are similar. Example 4 Tell whether the figures are similar. 10 cm A B 105° 75° 14 cm 14 cm 5 cm L M 115° 65° 7 cm 7 cm 75° 105° 65° D 115° C O N 10 cm 5 cm 7

Tell whether the figures are similar. Example 4 Tell whether the figures are similar. P Q 8 ft 70° 70° T 6 ft U 70° 70° 10 ft 10 ft 7.5 ft 7.5 ft 110° 110° W V 3.75 ft S 110° 110° R 5 ft 8

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 9

Tell whether the triangles are similar. 1. Lesson Quiz Tell whether the triangles are similar. 1. similar Tell whether the figures are similar. 2. not similar 10

Lesson Quiz for Student Response Systems 1. Which of the following triangles are similar? A. C. B. D. 11

Lesson Quiz for Student Response Systems 2. Which of the following figures are similar? A. B. 12