1. Similar Figures and Proportions
5-7
Similar Figures and Proportions
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
Warm Up
Find the cross products, 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. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
Problem of the Day
Every 8th telephone pole along a road has a red band painted on it. Every 14th pole has an emergency call phone on it. What is the number of the first pole with both a red band and a call phone? 56

4. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
Learn to use ratios to determine if two figures are similar.

5. Insert Lesson Title Here
Course 2
5-7
Similar Figures and Proportions
Insert Lesson Title Here
Vocabulary
similar
corresponding sides
corresponding angles

6. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
Octahedral fluorite is a crystal found in nature. It grows in the shape of an octahedron, which is a solid figure with eight triangular faces. The triangles in different-sized fluorite crystals are similar figures. Similar figures have the same shape but not necessarily the same size.

7. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
When naming similar figures, list the letters of the corresponding vertices in the same order. In the previous table ∆ABC ~ ∆DEF.
Writing Math

8. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.
82◦
Corresponding angles D E F
Corresponding sides A B C
55◦
43◦

9. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
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.

10. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
A side of a figure can be named by its endpoints, with a bar above. AB
Without the bar, the letters indicate the length of the side.
Reading Math

11. Additional Example 1: Determining Whether Two Triangles Are Similar
Course 2
5-7
Similar Figures and Proportions
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.

12. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
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.

13. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
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.

14. Additional Example 2 Continued
Course 2
5-7
Similar Figures and Proportions
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.

15. Additional Example 2 Continued
Course 2
5-7
Similar Figures and Proportions
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.

16. Similar Figures and Proportions
Course 2
5-7
Similar Figures and Proportions
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.

17. Check It Out: Example 2 Continued
Course 2
5-7
Similar Figures and Proportions
Check It Out: Example 2 Continued
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
MN corresponds to QR. NO RS
NO corresponds to RS. OP ST
OP corresponds to ST. MP QT
MP corresponds to QT.

18. Check It Out: Example 2 Continued
Course 2
5-7
Similar Figures and Proportions
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.

19. Similar Figures and Proportions Insert Lesson Title Here
Course 2
5-7
Similar Figures and Proportions
Insert Lesson Title Here
Lesson Quiz: Part I
Tell whether the figures are similar. 1.
59°
35°
86°
similar

20. Similar Figures and Proportions Insert Lesson Title Here
Course 2
5-7
Similar Figures and Proportions
Insert Lesson Title Here
Lesson Quiz: Part II
Tell whether the figures are similar. 2.
119°
55°
107°
79°
80°
135°
38°
not similar