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I know that congruent shapes have the same size and the rotations don't matter. I just want to know if congruent shapes can also be similar at the same time. I've seen that similar shapes have one shape that is a different size in comparison to another shape with proportional sides and the same angles. So is it safe to say that congruent shapes can also be similar?

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    $\begingroup$ What proportion would make them congruent? $\endgroup$ – N. F. Taussig Oct 24 '14 at 22:47
  • $\begingroup$ The proportions for congruent shapes are always the same. $\endgroup$ – user186302 Oct 24 '14 at 23:07
  • $\begingroup$ If you mean the proportion is equal to $1$, you are correct. Congruent shapes are a special case of similar triangles. $\endgroup$ – N. F. Taussig Oct 24 '14 at 23:12
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Yes; it is safe to say so. In general, if two shapes are congruent, then they must also be similar.

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