Question

Which polygons can be mapped onto each other by similarity transformations?

Answer 1

Solution:

Two polygons are said to be similar if ratio of their corresponding sides are same and their interior angles are congruent.

Consider Polygon 1 and Polygon 4

AB= DE= 8 units, AE= 6 units,

PT=QR= 4 Units, PQ= 3 Units

$\frac{AB}{PT}=\frac{DE}{QR}=\frac{AE}{PQ}=\frac{BC}{SR}=\frac{CD}{TS}$

So, Polygon 1 ≅ Polygon 4

Now, Consider Polygon 2 and Polygon 3

LM=KO=6 units, LK=4 units

GF= 4 units, GH=FJ =4 Units

As you can see that polygon 2 and polygon 4 doesn't have corresponding proportional sides i.e $\frac{6}{4}\neq \frac{4}{4}$.

So, Polygon 2  is not congruent to Polygon 4.

Answer 2

Polygon A,B,C,D,E and polygon L,M,N.O.K