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

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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

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

10. 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

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

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