Download Geometry 6.3

Geometry 6.3
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 6.1: Perimeters of
Similar Polygons
Corresponding Lengths in
Similar Polygons
 If two polygons are similar, then
 If two polygons are similar, then
the ratio of their perimeters is
equal to the ratios of their
corresponding sides.
 If KLMN  PQRS, then…
KL + LM + MN + NK KL LM MN NK
= = = =
PQ+QR+ RS + SP PQ QR RS SP
the ratio of any two
corresponding lengths is equal
to the scale factor of the similar
polygons