1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. 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

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

4. Vocabulary
similar
corresponding sides
corresponding angles

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

6. 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

7. 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

8. 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

9. 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.

10. 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.

11. 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.

12. Additional Example 2 ContinuedMN QR
MN corresponds to QR. NO RS
NO corresponds to RS. OP ST
OP corresponds to ST. MP QT
MP corresponds to QT.

13. 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.

14. 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.

15. 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.

16. 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.

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

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

19. 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

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

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