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Transcript
Similar Polygons
What are similar polygons?
Two polygons are similar if
corresponding (matching) angles are
congruent and the lengths of
corresponding sides are proportional.
Congruent Figures
• In order to be congruent, two figures
must be the same size and same
shape.
•
~
=
Similar Figures
• Similar figures must be the same
shape, but their sizes may be
different.
•
~
Angles and Sides in Similar Polygons
Angles
Sides
∠A ≅ ∠ E
AB ~ EF
∠B ≅ ∠ F
AC ~ EG
∠C ≅ ∠ G
BC ~ FG
A
ΔABC ~ ΔEFG
E
B
C
F
G
You can find the missing length of a side
in a pair of similar figures, by using
ΔRST ~ ΔUVW
proportions
R
U
x ft.
6 ft.
S
T
35 ft.
6
x
7 ft.
7
=
W
V
35
x = 30 feet
Solve for x.
40 in.
30 in..
12 in.
x in.
x
12
30
=
40
x = 9 inches
Solve for x.
Round to the
nearest tenth.
12 in.
4 in.
20 in.
x in..
4
12
x
=
20
x = 6.7 inches
Solve for x.
x
25 m.
14 m.
7 m.
7
14
=
25
x
x = 50 meters
17 in.
Solve for x.
Round to the
nearest tenth.
x
35 in.
15 in.
15
=
35
x
17
x = 7.3 inches
Determine the missing sides of the
triangle
39 in
? in
33 in
24 in
? in
8 in
Determine the length of the missing
side
• Two rectangles are similar. The first
is 4 in. wide and 15 in. long. The
second is 9 in. wide. Find the length
of the second rectangle.
Determine the length of the missing
side
• Two rectangles are similar. One is 5
cm by 12 cm. The longer side of the
second rectangle is 8 cm greater
than twice the shorter side. Find its
length and width.
Similar Figures
Which of the following is not a
characteristic of similar figures?
A. Proportional sides
B. Equal angle measurements
C. Same shape
D. Congruent side lengths
Similar Figures
• Are the figures below similar?
Explain.
Similar Figures
• Are the figures below similar?
Explain.