When you look at theorems involving right triangles, many textbooks will list three or four. But, in the end, most of those would have to be based on more general theorems such as Angle - Angle - Side. There are four theorems that apply to all triangles and thus using these for right triangles is just extra problems that might confuse some students. But, it is always good for the students to review old material and so this will cover all the theorems.
General Theorems:
Specific Theorems: