Download Geometry 7-2 Similar Polygons

Geometry 7-2 Similar Polygons
Similar polygons
have the same shape but not
always the same size. The formal definition is a little more
involved, though.
Two polygons are similar if and only if their corresponding
angles
are congruent
and their corresponding
side lengths
are proportional.
The symbol for similarity is ~.
The scale factor
is the common ratio of the side lengths.
The scale factor depends on the order of the comparison.
U
Q
4
6
6
9
P
8
R
T
V
12
The scale factor of PQR to TUV is 4/6 = 2/3.
The scale factor of TUV to PQR is 6/4 = 3/2.
Theorem 7.1 - Perimeters of Similar Polygons: If two
polygons are similar, then their perimeters have the same
scale factor as their sides.
If MNPQ ~ XYZW, find the scale factor of MNPQ to
XYZW and the perimeter of each polygon.
N
10
7
9
M
P W
8
Q
Z
4
X
Y
MNPQ : XYZW = 8:4 = 2:1
per MNPQ : per XYZW = 2:1
2 = 34
2x = 34
1 x
x = 17
per XYZW = 17 per MNPQ = 34
If NPQR ~ UVST, list all pairs of congruent angles, and
write a proportion that relates the corresponding sides.
P
N
S
V
Q
R
T
U
N~
= U, P ~
= V, Q ~
= S, R ~
= T
NP = PQ = QR = RN
UV VS ST TU
Find the value of each variable if JML ~ QST.
J
4
M
6x - 3
3y - 2
L
4 6x - 3
=
5
3
12 = 5(6x - 3)
12 = 30x - 15
27 = 30x
0.9 = x
S
5
3
T
2
Q
4 3y - 2
=
5
2
8 = 5(3y - 2)
8 = 15y - 10
18 = 15y
1.2 = y