Side Angle Side Theorem

Abbreviated as SAS, the side angle side theorem tells us:
If two triangles have two congruent sides and a congruent angle, then the triangles are congruent.

Let’s look at theoretical triangles T₁ and T₂. T₁ has two sides measured to be 3 and 5 long and an angle measured to be 90°. T₂ also has two sides measured to be 3 and 5 long and an angle measured to be 90°. The SAS Theorem tells us that T₁ and T₂ must be congruent because they have two side lengths in common and an angle measurement in common.

The SAS Theorem is especially useful for saving time when finding the third side and other two angles of a triangle if there is a congruent triangle where those values are already known.