No, complementary angles are not always congruent. By definition, complementary angles are two angles whose measures add up to 90 degrees. While two angles can be congruent—meaning they have the same measure—they do not have to be.
For example, consider a 30-degree angle and a 60-degree angle. These two angles are complementary because their sum is 90 degrees (30 + 60 = 90). However, they are not congruent since one measures 30 degrees and the other measures 60 degrees.
In contrast, two angles can be both complementary and congruent if they each measure 45 degrees (45 + 45 = 90). But this is just one specific case. Thus, the general answer is that complementary angles do not have to be congruent; they simply need to add up to 90 degrees.