# The SAS Criterion

Now, we will start discussing the various conditions under which two triangles can be congruent.

The simplest criterion for the congruence of two triangles is the **Side-Angle-Side** criterion. This states that if two sides of one triangle, and the angle contained between these two sides, are *respectively* equal to two sides of another triangle and the angle contained between them, then the two triangles will be congruent. Let us understand this through a diagram.

Consider the following two triangles, **ABC** and **DEF**:

Suppose that AB = DE, AC = DF. and ∠A = ∠D. Can you intuitively feel that the two triangles will be congruent? Suppose that you were to try and (exactly) superimpose ∆DEF.on ∆ABC. You would do this by moving the vertex D onto the vertex A., and aligning one side, say DE, with AB. Then, because ∠A = ∠D, the side DF will automatically become exactly aligned with the side AC, and so E would be lying on top of B, and F would be lying on top of C. This means that DF will also be exactly aligned with and equal to BC.

Thus, you would be able to exactly superimpose ∆DEF on ∆ABC – the two triangles are thus congruent.

The SAS criterion is taken to be an axiom.