Do you mean similar?

what happen on the least cut? Necessarily the two triangles are congruents, make cases we obtain that the triangles have an angle of 90°, so the triangles that we want that are congruents, are triangles rectangles. It's easy to see that there are examples for triangles rectangles and isosceles, but I don't know how to prove for other triangles (maybe using that the short pieces are triangles rectangles)

gabrielghx wrote: Do you mean similar? I think @anantmudgal90 does mean similar instead of congruent, because if you keep dividing them into 2 then they can't be congruent since everything (except angles), including area, is halved. They will be similar, though.