# Prove that the similarity of polygons is an equivalence relation.

Prove that the similarity of polygons is an equivalence relation.
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Step 1
Let A, B and C are polygons. It is known that A is similar to A and so similarity between polygons is reflexive.
Step 2
If A is similar to B then B similar to A and so similarity between polygons is symmetric.
Step 3
Similarly, If A and B are both similar to C then A and B are similar as figures similar to the same rectilinear figure is also similar to one another and so similarity between polygons is transitive.
Step 4
Therefore, the similarity of polygons is an equivalence relation.