Adjoining angles are two angles that have a common vertex and a common side. If two lines intersect, they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Adjoining angles are angles that come from the same vertex. They are examples of adjacent angles.

The vertical angles are congruent (equal).

Which is the relationship between adjacent and congruent angles?

No necessary connection exists between adjacent and congruent angles. Adjoining angles are two angles that have a shared apex and a shared side. Thus, the concept relates to two adjacent angles, the line they make meets in the same place.

There is no need for their actions to be related to each other. A congruent angle is an angle that has the same dimension. There is no need for their sites to be related to each other. Any two adjacent angles can also be congruent, but there is nothing that will require them.

The two congruent angles can also be side by side, but there is nothing that needs them. But I believe that adjacent angles are two angles that have a joint bone between them. A congruent angle is two angles that are the same in angle (degrees, radians, cats, pups, whatever you are using for angle measurement at the moment).

There' s no actual relationship between the two of them. Matching angles may or may not be adjacent and adjacent angles may or may not be matching. I can only imagine a "relationship" where both angles are, which in my opinion is not much help.