No, complementary angles aren't normally congruent.
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Vertical angles must be congruent so if they are complementary, they must be 45 degrees to be complementary.
not all congruent angles are vertical angles. Vertical angles must share a vertex.
congruent; congruent
None! If the angles are not congruent then the shapes are not similar of congruent. But that is not a problem. The angles of an equilateral triangle are not congruent to the angles of a square but that does not mean that you cannot work with equilateral triangles or squares!
Two angles are said to be congruent if they are equal.