Most general triangle:
3 non-zero angles
3 non-zero edges
Sum of angles: 180 degrees

Isosceles triangle
Invariant of general triangle
2 edges of equal length

Equilateral triangle:
Invariant of isosceles triangle
3 edges of equal length

Right triangle:
Invariant of general triangle
Pythagoras

Isosceles right triangle:
Invariant of isosceles triangle
Invariant of right triangle