Trent Carpenter
2021-02-14
Answered

Prove that the similarity of polygons is an equivalence relation.

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timbalemX

Answered 2021-02-15
Author has **108** answers

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.

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.

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