Final answer:
Congruent angles must have the same angle measure regardless of their orientation or position. They are not defined by sharing a vertex or a side, nor by summing to 90°, which are characteristics of adjacent angles and complementary angles, respectively.
Step-by-step explanation:
Congruent angles must satisfy the condition that they have the same angle measure. This means that regardless of the position or orientation of the angles, if two angles are congruent, their angle measures are equal. For example, if one angle measures 30°, another angle that is congruent to it must also measure 30°.
It's important not to confuse congruent angles with adjacent angles or complementary angles. Adjacent angles share a vertex and a side, but they do not need to have the same measure to be adjacent. Complementary angles are two angles whose measures add up to 90°, but they do not have to be congruent to be complementary.