# Are two congruent polygons always similar?

Congruent shapes are always similar

The word 'congruent' means identical in all aspects.. It is the geometry equivalent of 'equal'.

Congruent figures have the same size, the same angles, the same sides and the same shape. They are IDENTICAL! As a transformation we could say that the image maps onto the figure exactly.

The only things that can be different about congruent shapes are their position and orientation. (and the names of the vertices).

Similar figures have the same angles which means that they have the same shapes, but they differ in size. However, the sides are still in the the same ratio.

Congruent shapes are always similar , but similar shapes are usually not congruent - one is bigger and one is smaller.

In congruent shapes, the ratio of the corresponding sides is 1:1.

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Yes. Congruent polygons are similar.

Start with the definition of congruence. Congruent objects on a plane are those that can be transformed one into another by any combination of the following transformations:

- rotation around some point as a center,
- translation (shift) in certain direction,
- symmetry around some axis.

Continue with a definition of similarity. Similar objects on a plane are those that can be transformed one into another by any combination of the following transformations:

- scaling using some point on a plane as a center and some real number as a factor of scaling,
- rotation around some point as a center,
- translation (shift) in certain direction,
- symmetry around some axis.

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Yes, two congruent polygons are always similar. Congruent polygons have exactly the same shape and size, meaning that all corresponding angles are congruent and all corresponding sides are of equal length. Since similarity is defined as having the same shape but not necessarily the same size, if two polygons are congruent, they must also be similar. Therefore, congruent polygons are a subset of similar polygons.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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