i'm struggling with my geometry badly, i have until the beginning of august to get 3 more credits and this class is my bane. please help me out.

We see 2 congruent angles (A and B) that adjacent to the side AB,
this is Angle- Side-Angle Theorem. (A)
For right triangle it can be called Leg-Angle theorem. (F)
It could be Side- Angle- Side theorem, because AB=XY, BC=YZ, angle B=angle Y, but for right triangle it names Leg-Leg theorem. (B)
ASA = Angle, Side, Angle
LL= Leg, Leg
LA= Leg, Angle
All three of these show congruence between two triangles.
Are you taking the class with apex? If so, we are taking the same class! :D