you still need to assume 'among right triangles, two of them are said congruent iff their two sides are respectively of equal length'

to be a definition or a postulate in the proof in 《周髀算經》.

i can also take

'among arbitrary triangles, two of them are said congruent iff their two sides are respectively of equal length and the angles in between are equal'

as a definition or a postulate in Euclid's proof.

the only difference is the angle.