Triangles which are on the same base and between the same parallels are equal to one another.  Let $ABC$ and $DBC$ be triangles on the same base $BC$, and between the same parallels $AD$ and $BC$. I say that triangle $ABC$ is equal to triangle $DBC$. <prf> Thus, triangle $ABC$ is equal to triangle $DBC$.Thus, triangles which are on the same base and between the same parallels are equal to one another.