Download Geometry 6.3

Geometry 7.2
SWLT: Use Proportions to identify similar polygons
Similar Polygons
 Two or more polygons are similar, if corresponding
angles are congruent and corresponding side lengths
are proportional
 Same as when comparing and proving congruency,
order is important.
ABC  DEF
1. List all pairs of Congruent Angles
A  D, B  E, C  F
2. Confirm that the ratios of the
corresponding side lengths are equal.
AB 10 2 BC 8 2 CA 12 2
= = , = = , = =
DE 15 3 EF 12 3 FD 18 3
B
8
10
A
12
C
E
2. Write the ratios of the corresponding
side lengths in a statement of
proportionality
AB BC CA
=
=
DE EF FD
12
15
F
18
D
BCD  RST, Find the value of x
 Write a Proportion
BC CD
=
RS ST
 Substitute
 Cross Multiply
C
12 13
=
24 x
12
13
S
12x = 13(24)
B
5
D
 Solve for x
12x = 312
24
x
x = 26
R
10
T
Theorem: Areas of Similar
Polygons
 If two polygons are similar, then
8
K
the ratio of their areas are equal
to the ratios of their
corresponding sides.
 If KLMN  PQRS, then…
AreaPQRS PQ
=
AreaKLMN KL
A = 24
N
M
P
15 PQ
=
24
8
 15(8) = 24PQ
 120 = 24PQ
 PQ = 5
L
Q
A = 15
S
R