Here is a polygon. The side lengths are: AB= 18 units, BC= 12 units, CD= 6 units, and DA= 24 units.

1. If polygon ABCD is dilated using center A and scale factor LaTeX: \frac{1}{2}1 2, what will be the side lengths of dilated polygon EFGH?
EF= ____, FG= ____, GH= ____, HE= ____

2. If polygon ABCD is dilated using center D and scale factor LaTeX: \frac{1}{3}1 3, what will be the side lengths of dilated polygon IJKL?

IJ= ____, JK= ____, KL= ____, LI= ____

3. How do you know that polygons EFGH and IJKL are similar?

Answer:Given : Polygon side lengths are: AB= 18 units, BC= 12 units, CD= 6 units, and DA= 24 units.  

polygon ABCD is dilated using center A and scale factor  1/2

polygon ABCD is dilated using center D and scale factor  1/3

To Find :

side lengths of dilated polygon EFGH

EF= ____, FG= ____, GH= ____, HE=

side lengths of dilated polygon IJKL?

IJ= ____, JK= ____, KL= ____, LI= ____

Solution:

AB= 18 units, BC= 12 units, CD= 6 units, and DA= 24 units.  

EF=  AB/2  = 18/2 = 9

FG = BC/2 = 12/2 = 6

GH = CD/2 = 6/2 = 3

HI = DA/2 = 24/2 = 12

IJ= AB/3 = 18/3 = 6

JK = BC/3 = 12/3 = 4

KL= CD/3 = 6/3 = 2

LI =  DA/3 = 24/3 = 8

polygon  EFGH is Dilated from polygon ABCD

Hence polygon  EFGH ≈ polygon ABCD

polygon  IJKL is Dilated from polygon ABCD

Hence polygon   IJKL ≈ polygon ABCD

As polygon ABCD   ≈  polygon   IJKL  & polygon  EFGH

=>   polygon  EFGH ≈ polygon   IJKL

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