Geometry/Congruency and Similarity
Congruent shapes are the same size with corresponding lengths and angles equal. In other words, they are exactly the same size and shape. They will fit on top of each other perfectly. Therefore if you know the size and shape of one you know the size and shape of the others. For example:
Each of the above shapes is congruent to each other. The only difference is in their orientation, or the way they are rotated. If you traced them onto paper and cut them out, you could see that they fit over each other exactly.
Having done this, right away we can see that, though the angles correspond in size and position, the sides do not. Therefore it is proved the triangles are not congruent.
Similar shapes are like congruent shapes in that they must be the same shape, but they don't have to be the same size. Their corresponding angles are congruent and their corresponding sides are in proportion.