** Congruent vs Similar **

In mathematics, terms ‘similar’ and ‘congruent’ are most often used with plane figures. They describe the relation between shapes. Identifying similarity or congruence between two or more figures will be helpful in the calculation and design works involving figures.

**Similar**

Two figures are said to be similar, if they have the same shape. However, they may be different in size. Therefore, the area of two similar plane figures may not be equal. For example, two triangles are said to be similar, if their corresponding angles are equal, or the ratios between their corresponding bases are equal. We can draw infinitely many similar triangles with equal angles but with different sizes. There can be same, smaller, or larger size of similar figure compare to the original. Symbols ‘= or_{ ˜}’ is used to denote similarity. We can make a similar figure of a given figure by multiplying its each side by the same number. For an example, when you enlarge a photograph or when you shrunk a photograph to make a slide, you have made a similar photograph.

**Congruent**

Two figures are congruent, if they are similar in shape, as well as, similar in size. Therefore, in two congruent figures all the corresponding angles and sizes of the corresponding bases are equal to each other. So any two figures, which are congruent, are exactly the same. We can form a congruent figure to a given figure by rotating the original. The symbol to represent congruency is ‘≡’.

· Similar figures are the same in shape, while congruent figures are the same in both shape and size. · The areas of two similar figures may be different. However, the areas of two congruent figures are equal. · The ratios between the corresponding sides of two similar figures are equal. The ratios between the corresponding bases of two congruent figures are always one. |