Similar Figures TeacherTwins©2015

Warm Up What is the scale factor for the following scales? 1). 4 in = 3 feet 2). 4 cm = 2 m 3). 3 feet = 4 yards 4). 3 in = 2 yards 5). A truck is 8 ft. long. In a scale drawing it is 2 inches long. What is the scale? What is the scale factor? 1/50 1/9 1/24 1/4  

Similar Figures are figures that have the same shape but not necessarily the same size. For figures to be similar they must meet the following requirements: The measure of their corresponding angles are equal. The ratios of the lengths of the corresponding sides are proportional.

Identifying Corresponding Angles B E F G H D C Corresponding angles are a pair of matching angles that are in the same spot in two different shapes. < A corresponds to < G < D corresponds to < E < B corresponds to < H < C corresponds to < F The arcs drawn in the angles show which angles are equal or congruent. The angles with one arc are congruent and the angles with 2 arcs are congruent. Congruent angles can also be shown using degrees.

Identifying Corresponding Sides A F E B C D Corresponding sides are a pair of matching sides that are in the same spot in two different shapes. AB corresponds to DE BC corresponds to EF CA corresponds to FD

Determining If Figures are Similar Example 1: A C E G 5 in 2 in B D H F 4 inches 7 inches Are the following figures similar? Explain why or why not? Are corresponding angles equal? Are corresponding sides proportional? All angles in a rectangle are 90 degrees, so corresponding angles are equal. Corresponding sides are not proportional because the ratio of corresponding side lengths are not equal. These are not similar.  

Determining If Figures are Similar Example 2: 60° 60° 4 cm 6 cm 3 cm 4.5 cm 90° 30° 90° 30° 6 cm 9 cm Are these triangles similar? Explain why or why not.  

Practice 12 in 12 in 6 in 6 in 10 m 14 m 8 in 4 in 18 ft. 12 ft. 125° Si Practice Are the following figures similar? Explain why or why not. 1). 2). 50° 12 in 12 in 50° 6 in 6 in 10 m 14 m 65° 65° 65° 65° 8 in 4 in 3). 18 ft. 12 ft. 125° 125° 45° 45° 10 ft. 10 ft. 7 ft. 7 ft. 55° 55° 135° 135° 8 ft. 22 ft.

Practice Si Are the following figures similar? Explain why or why not. 1). 2). 50° 12 in 12 in 50° 6 in 6 in 14 m 10 m 65° 65° 65° 65° 8 in 4 in Yes, corresponding sides are proportional and corresponding angles are equal. Yes, corresponding sides are proportional and corresponding angles are equal. 3). 18 ft. 12 ft. 125° 125° 45° 45° 10 ft. 10 ft. 7 ft. 7 ft. 55° 55° 135° 135° 8 ft. 22 ft. No, corresponding sides are not proportional and corresponding angles are not equal.

Si Closure Are all squares similar? Explain why or why not. Use examples to support your claim.