Definition: The ASA criterion states that if two angles and the included side of one triangle match those of another, the two triangles are congruent.
What is the included side?
It is the side between the two known angles. If the angles are at vertices B and C, the included side is BC.
Why does it work?
Once the two angles and the side between them are fixed, the other two sides must meet at exactly one point. The shape is forced.
Example. In triangle PQR, angle P = 40 degrees, angle Q = 75 degrees, and PQ = 9. In triangle XYZ, angle X = 40 degrees, angle Y = 75 degrees, and XY = 9. Segment PQ lies between angles P and Q, and XY lies between X and Y, so the triangles are congruent by ASA. Then angle R and angle Z are both 65 degrees.
What errors occur?
Using a side that is not between the angles. That configuration is AAS, which also works but must be named correctly. Another error is to assume two angles alone are enough; two angles give a similar triangle, not a congruent one. In proofs, the angles often come from alternate interior angles or a common bisector.