Teacher resources icon

The SSS congruence test

Suppose first that we are asked to construct a triangle ABC in which
AB = 12 cm and AC = 5 cm.

There are infinitely many ways to do this, because the two sides can remain joined at A, but flap around. Three such triangles are shown below, and they are clearly not congruent.

This shows that just knowing that two pairs of sides are equal is not enough information to establish congruence.

Three triangles all different but each with side lengths 5cm and 12cm.

Constructing a triangle with three given sides

When all three sides of a triangle are given, however, there is no longer any freedom of movement, and only one such triangle can be constructed up to congruence.

For example, a triangle with side lengths 3 cm, 4 cm and 5 cm is unique up to congruence.

Triangle with side lengths 3cm, 4cm and 5cm.