Congruent and Similar Figures

Similar-geometric-shapes

Figures shown in the same color are similar

Similarity is an idea in geometry. It means that two polygons, line segments, or other figures have the same shape. Similar objects do not need to have the same size. Two shapes are similar if their angles have the same measure and their sides are proportional. Two circles, squares, or line segments are always similar.

Triangles are special in similarity. This is because triangles can be similar if only their angles are equal, or only their sides are proportional. All other polygons must meet both of the conditions.

Similarity is very similar to congruence. Congruent shapes have the same sides and angles. In fact, all shapes that are congruent to each other are also similar.

Congruence

An example of congruence. The two shapes on the left are congruent. The third is similar to the first two, but not congruent, because it needs to be grown to match them. The last shape is neither similar nor congruent

Two geometrical shapes are congruent if one can be moved or rotated so that it fits exactly where the other one is. If one of the object has to change its size, the two objects are not congruent: they are just called similar.

If two figures or objects are congruent, they have the same shape and size; but they can be rotated, moved, mirror imaged (reflected) or translated, so that it fits exactly were the other one is.

Examples

  • all squares that have the same length of their sides are congruent.
  • all equilateral triangles that have the same length of their sides are congruent.

(Source – one – two)

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