Transcript Similar Figures

Similar and
Congruent Figures
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
Are these figures similar and/or
congruent and why?
Are these figures similar and/or
congruent and why?
Are these figures similar and/or
congruent and why?
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.