Question

two Triangles having the same base or equal base and equal area lie between the same parallels?

Answer 1

yes it is true that two triangles having the same base or equal base and equal area lie between the same parallels.it is theorem 9.3.it is converse of 9.2 theorem which said that two triangles having the same base and lie between same parallels are equal in area.
the proof is given in the maths ncert class 9.

Answer 2

Yes.
if two triangles having same base and same area then they must be between same parallel lines.