write the two conditions for two polygons of same number of sides to be similar
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For any two regular polygons with the same number of sides: They are always similar. Since they have the sides all the same length they must always be in the same proportions, and their interior angles are always the same, and so are always similar.
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Similar polygons: Two polygons are called similar if their corresponding angles are equal and the ratio of the corresponding sides of two polygons are equal. Therefore, if two polygons of the same number of sides are similar if their corresponding angles are equal and their corresponding sides are proportional.
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