For two triangles to be similar, they must have the same shape, which means that their corresponding angles must be equal. In fact, it is sufficient for just one pair of corresponding angles to be equal to establish similarity. However, the common approach is to check for all three pairs of corresponding angles.
Therefore, to determine that two triangles are similar, you need to establish that at least two angles in one triangle are equal to two angles in another triangle. If two angles in one triangle are the same as two angles in another triangle, the third angles will also be equal due to the triangle sum theorem (which states that the sum of the angles in a triangle is always 180 degrees).
In summary, while all three angles correspondingly must be equal for a full similarity confirmation, establishing the equality of just two angles is enough for the triangles to be considered similar.