Congruent Shapes
Congruent shapes are objects that are both the same shape and exactly the same size.
Triangles ABC and DEF in the image above, for example, are congruent because they are both triangles, the respective angles are the same, and the respective sides are the same length. If one were to place the image of Triangle ABC on top of the image of Triangle DEF, the images would line up exactly, and this would be the case for all congruent shapes.
To be congruent, the shapes do not need to have the same orientation, but rather can be facing different directions or flipped over.
The triangles in the diagram below have the same angles and the same side lengths, so they are congruent even though they are facing a different direction. It does not matter if the figure is rotated or flipped over. As long as the angles and side lengths are the same, the shapes are considered congruent. Congruent shapes are always also similar.
Similar Shapes
Similar shapes are objects that are the same shape, but not the same size. In the diagram above, triangles ABC and EGF are similar because they have the same shape and the same angles. They are not congruent because ABC is clearly smaller than EGF.
Likewise, the two rectangles seen below are similar because they are both rectangles with proportional sides, but the sizes are different so they are not congruent.
Similar vs. Congruent
While all congruent shapes are also similar, all similar shapes are not congruent. Shapes are both congruent and similar when they have the same shape and the same size.
One could be placed right over the other (known as being “superimposed”) and they would be identical – same angles, same side lengths, same shape.
Shapes are similar if they have matching corresponding angles and their corresponding lines are proportional. They can, however, be different sizes. Figures are considered to be both congruent and similar if they are both the same size and the same shape, regardless of orientation. They may be rotated or flipped, but as long as the size, shape, and angles are all maintained, the objects are considered both congruent and similar.