I'm doing some Geometry work and I'm wondering how you would prove that two angles are congruent. I know that they are of the same angle size but I'm not sure why or how to prove it exactly.
I'm not sure what exactly you're looking for. Since, you have mentioned about Vertical Angle theorem, here it is. When two lines intersect at a point. The vertically opposite angle are equal.
In this case, you see $\angle CXB= \angle AXD$ eventually other pair is equal.
Oh right, Angle 1 is congruent to angle 3 because they are verticle angles right?
1 + 2 = 180
2 + 3 = 180
1 + 2 = 2 + 3
1 = 3