Similar Figures and Proportions

1. Similar Figures and Proportions
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation

2. Warm Up
Find the cross products, then tell whether the
ratios are equal.
Course 2
5-7 Similar Figures and Proportions
1.
16
6
, 40
15
2.
3
8
, 18
46
3.
8
9
, 24
27
4.
28
12
, 42
18
240 = 240; equal
216 = 216; equal
504 = 504; equal
138 = 144; not equal

3. 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
Course 2
5-7 Similar Figures and Proportions

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

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

6. 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. 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. 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
82◦
55◦43◦ 55◦43◦

9. 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. 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. Identify the corresponding sides in the pair of triangles.
Then use ratios to determine whether the triangles are
similar.
Additional Example 1: Determining Whether Two
Triangles Are Similar
Course 2
5-7 Similar Figures and Proportions
A C
B
10 in
4 in 7 in
D
E
F
16 in
28 in
40 in
AB corresponds to DE.
BC corresponds to EF.
AB
DE
=
? BC
EF
=
? AC
DF
4
16
7
28
10
40
1
4
1
4
1
4
Since the ratios of the corresponding sides are equivalent, the
triangles are similar.
Write ratios using the corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
=
?
=
?
AC corresponds to DF.
=
?
=
?

12. Identify the corresponding sides in the pair of triangles.
Then use ratios to determine whether the triangles are
similar.
Check It Out: Example 1
Course 2
5-7 Similar Figures and Proportions
A C
B
9 in
3 in 7 in
D
E
F
9 in
21 in
27 in
AB corresponds to DE.
BC corresponds to EF.
AB
DE
=
? BC
EF
=
? AC
DF
3
9
7
21
9
27
1
3
1
3
1
3
Since the ratios of the corresponding sides are equivalent, the
triangles are similar.
Write ratios using the corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
=
?
=
?
AC corresponds to DF.
=
?
=
?

13. Tell whether the figures are similar.
Additional Example 2: Determining Whether Two
Four-Sided Figures are Similar
Course 2
5-7 Similar Figures and Proportions
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
MN
QR
MN corresponds to QR.
NO
RS
OP
ST
MP
QT
NO corresponds to RS.
OP corresponds to ST.
MP corresponds to QT.

15. Determine whether the ratios of the lengths of the
corresponding sides are proportional.
Additional Example 2 Continued
Course 2
5-7 Similar Figures and Proportions
Write ratios using
corresponding sides.
Substitute the length of
the sides.
Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the figures are similar.
MN
QR
=
? NO
RS
=? OP
ST
=? MP
QT
6
9
=
? 8
12
=
? 4
6 =
? 10
15
2
3
= 2
3
= 2
3
= 2
3
? ? ?

16. Tell whether the figures are similar.
Check It Out: Example 2
Course 2
5-7 Similar Figures and Proportions
The corresponding angles of the
figures have equal measure.
100 m
80 m
60 m 47.5 m
80°
90°
125°
65°
M P
N
O
400 m
320 m
190 m240 m
80° 65°
90°
125°
Q T
R S
Write each set of
corresponding sides as a ratio.

17. Check It Out: Example 2 Continued
Course 2
5-7 Similar Figures and Proportions
MN
QR
MN corresponds to QR.
NO
RS
OP
ST
MP
QT
NO corresponds to RS.
OP corresponds to ST.
MP corresponds to QT.
100 m
80 m
60 m 47.5 m
80°
90°
125°
65°
M P
N
O
400 m
320 m
190 m240 m
80° 65°
90°
125°
Q T
R S

18. Determine whether the ratios of the lengths of the
corresponding sides are proportional.
Check It Out: Example 2 Continued
Course 2
5-7 Similar Figures and Proportions
Write ratios using corresponding
sides.
Substitute the length of the
sides.
Simplify each ratio.
Since the ratios of the corresponding sides
are equivalent, 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 m240 m
80° 65°
90°
125°
Q T
R S
MN
QR
=
? NO
RS
=
? OP
ST
=
? MP
QT
60
240 =
? 80
320 =
? 47.5
190 =
? 100
400
1
4
= 1
4
= 1
4
= 1
4
? ? ?

19. Lesson Quiz: Part I
Insert Lesson Title Here
Course 2
5-7 Similar Figures and Proportions
Tell whether the figures are similar.
1.
similar59°
59°
35°
35°
86°
86°

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