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Similarity in geometry refers to a relationship between two shapes that have the same form but not necessarily the same size—meaning one shape is an enlarged or reduced version of the other, with all corresponding angles equal and all corresponding side lengths proportional. This concept matters because it allows us to understand how shapes relate to each other and is useful in practical applications like maps, blueprints, and photography, where we need to represent objects at different scales while preserving their essential proportions.
AI-generated from the Wikipedia summary — may contain errors.
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Similar figures In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other.
For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other. This is because two ellipses can have different width to height ratios, two rectangles can have different length to breadth ratios, and two isosceles triangles can have different base angles.