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Applications of Congruent and Similar Shapes The rectangles would also be similar even if one of them were rotated. Even though one of the rectangles might be bigger or smaller than the other, their angles would still be the same. Even if one of the triangles was rotated, or if the shape or sizes changed, the shapes would still not be congruent.Īn example of a similar shape, on the other hand, would be two rectangles. Examples of Congruent and Similar ShapesĪn example of congruent shapes would be two triangles with equal angles, as long as they were exact mirror images of each other. Therefore, it is important to understand the difference between the two concepts so that they can be correctly identified when solving geometric problems. Moreover, orientation does not affect similarity, while it does affect congruent shapes. All sides and angles must be the same for congruent shapes, while this is not necessarily true for similar shapes. The major difference between congruent and similar shapes is that congruent shapes must have the same size and shape, while similar shapes do not. How Can Congruent and Similar Shapes be Differentiated? Two triangles can be similar even if one is rotated differently than the other as long as the angles between the triangles are the same. It is also important to note that similarity does not depend on orientation either. For example, if one shape is larger or smaller than the other, the angles will still be the same between them. However, they will have certain proportions in common and the angles in each shape will be the same. Similar shapes are not necessarily the same size and shape. Similarity is another type of geometrical relationship between two shapes. For example, two squares may be the same size and have the same angles, but if one of them is rotated differently than the other, they will not be congruent. Therefore, if two shapes have the same sides and angles but different sizes, they are not congruent.Īnother important thing to note about congruent shapes is that they must also have the same orientation. In order for two shapes to be congruent, all angles and all sides must be the same. They can also be thought of as mirror images of each other. Congruent shapes are shapes that have identical size and shape.