Similar Polygons• Similar Polygons: all corresponding angles are
congruent and the sides are proportional.
When 2 polygons are similar
The symbol used when 2 figures are similar is: ~When you know 2 figures are similar you must name the corresponding angles in the same order.
Name the corresponding angles, then the ratios of the corresponding sides.
ŸA,ŸDŸB,ŸEŸC,ŸF
DE
AB
EF
BC
DF
AC
Name the corresponding angles, then the ratios of the corresponding sides.
ŸR,ŸWŸS,ŸVŸT,ŸU
WV
RS
ST
VU
WU
RT
Name the corresponding angles, then the ratios of the corresponding sides.
ŸC,ŸMŸD,ŸJŸE,ŸK
MJ
CD
JK
DE
KL
EF
ŸF,ŸL
ML
CF
Name the corresponding angles, then the ratios of the corresponding sides.
ŸP,ŸZŸQ,ŸWŸR,ŸX
ZW
PQ
WX
QR
XY
RS
ŸS,ŸY
ZY
PS
Scale factor
• The scale factor is the simplified ratio of corresponding sides of a similar polygon
3
2
6
4
3
2
9
6
Determine whether the polygons are similar…then state a similarity statement, and find the scale factor.
yes
„ABC~„FDE„ACB~„FED„BCA~„DEF„BAC~„DFE„CAB~„EFD„CBA~„EDF
Determine whether the polygons are similar…then state a similarity statement.
yes
„ABC~„FDE„ACB~„FED„BCA~„DEF„BAC~„DFE„CAB~„EFD„CBA~„EDF
Use the scale factor to find the length of a side.
204
34
3
12
9
x
rscalefactoNM
ED
Cross multiply3(20) = 4x
60 = 4x15 = x
Find the scale factor, then find the lengths of the sides, and the perimeter.
factorscale4
3
12
9
x
15
4
3
y
21
4
3
x
y
3x = 4(15)3x = 60x = 20
3y = 4(21)3y = 84y = 28
P= 60
P= 45
Find the scale factor, then find the lengths of the sides, and the perimeter.
factorscale5
3
35
21
255
3 x
205
3 y
x
y
3(25) = 5x75 = 5x15 = x
5y = 3(20)5y = 60y = 12
P= 100 P= 60
z
205
3 z
5z = 3(20)5z = 60z = 12