Corresponding sides and corresponding angles

In geometry, a number of tests for congruence and similarity involve comparing corresponding sides. In such tests, each side in one figure is paired with a side in the second figure, taking care to preserve the order of adjacency.

For example, if one figure has sequential sides a, b, c, d, and e and the other figure has sequential sides v, w, x, y, and z, and if b and w are corresponding sides, then side a (adjacent to b) must correspond to either v or x (both adjacent to w). If a and v correspond to each other, then c corresponds to x, d corresponds to y, and e corresponds to z; hence the i^th element of the sequence abcde corresponds to the i^th element of the sequence vwxyz for i=1, 2, 3, 4, 5. On the other hand, if in addition to b corresponding to w we have c corresponding to v, then the i^th element of abcde corresponds to the i^th element of the reverse sequence xwvzy.

Typically, congruency tests look for pairs of corresponding sides to be equal in length, and similarity tests look at whether the ratios of the lengths of each pair of corresponding sides are equal.

If there are corresponding sides, there would also be corresponding angles.