19
Similar Polygons 6.3 Yes: ABCD ~ FEHG No 2 3 PQ = 12 mQ = 30
Similar Polygons6.3
Yes: ABCD ~ FEHGNo
2
3
PQ = 12
mQ = 30
Similar Polygons6.3
Chapter 6SimilaritySection 6.3
Similar Polygons
Similar Polygons6.3
Definition Similar Polygons
Trapezoid ABCD ~ Trapezoid PQRS
B Q, A P, C R, D SBC BA AD CD
QR QP PS RS
Similar Polygons6.3
S C
T D
U E
ST
CD
Corresponding components must line up in the similarity statement
TU
DE
SU
CE
Similar Polygons6.3
L G
M H
N I
LM
GH
Corresponding components must line up in the similarity statement
MN
HI
LN
GI
Similar Polygons6.3
Q A
R B
S C
T D
QR
AB
Corresponding components must line up in the similarity statement
RS
BCST
CD
QT
AD
Similar Polygons6.3
Definition: Scale Factor
The ratio of any two corresponding sides of similar polygons.
Scale Factor6
4 3
2
4
6 2
3Scale Factor
Similar Polygons6.3
Solution
1. Find the Scale Factor
2. Find the ratio of XY and BE
3. Set up a proportion and solve for XY
CD
XY
XY3
32
32
Scale Factor:
Ratio of CD and XY
Proportion
2(XY) = 9
29
XY
3
XY
Similar Polygons6.3
3D Y
m Y + m X = 180
Consecutive Interior Angle Theorem
m Y + 117 = 180
m Y = 63
m D = 63
Similar Polygons6.3
3p = XW + WZ + YZ + XY
29
29
Need to find YZ
YZ6
32
2(YZ) = 18
YZ = 9
9p = 6 + + 9 +
29
29
p = 24
Similar Polygons6.3
3
29
29
9Ratio of the perimeters = scale factor
23
BCDEPerimeterWXYZPerimeter
Similar Polygons6.3
Assume the angles are congruent
48
4
)2(4
422
22
Similar Polygons6.3
Assume the angles are congruent
85
Similar Polygons6.3
x
x + x + 42 = 180
2x + 42 = 180
2x = 138
x = 69
8 10
10 y
8y = 100
100
8y
25
2
Similar Polygons6.3
y = 11
72
x = 72
Similar Polygons6.3
Ratio of the perimeters = scale factor85
DEFPerimeterABCPerimeter
Fill in what you know and solve85
96x
8x =480
x = 60
State your answer The perimeter of ABC = 60 inches
Similar Polygons6.3
Ratio of the perimeters = scale factor 1560
14
A
B C
D
F G
E H
18
18
Find FGFG18
14
4(FG) = 18
418
FG 29
4½
4½
Similar Polygons6.3
A
B C
D
F G
E H
18
18
EF = GH and FG = EH
4½
4½
p = EF + FG + GH + EH
p = EF + FG + EF + FG
p = 2(EF) + 2(FG)
15 = 2(EF) + 2(4½)
15 = 2(EF) + 9
6 = 2(EF)
3 = EF
3 3
Similar Polygons6.3
HW #Pg
