Harmonious Triangles

Call $\triangle ABC$ harmonious if, after folding along its three midsegments, the four small triangles can be assembled into a (non-degenerate) tetrahedron. With $A, B, C$ the angles of the triangle, determine, with proof, which of the following conditions guarantee a harmonious triangle:

1. $A : B : C = 7 : 20 : 25$; 2. $\sin A : \sin B : \sin C = 7 : 20 : 25$; 3. $\cos A : \cos B : \cos C = 7 : 20 : 25$; 4. $\tan A : \tan B : \tan C = 7 : 20 : 25$.