If a parallelogram has the same base as a triangle, and is between the same parallels, then the parallelogram is double (the area) of the triangle. For let parallelogram $ABCD$ have the same base $BC$ as triangle $EBC$, and let it be between the same parallels, $BC$ and $AE$. I say that  parallelogram $ABCD$ is double (the area) of triangle $BEC$.  <prf> So parallelogram $ABCD$ is also double (the area) of triangle $EBC$.Thus, if a parallelogram has the same base as a triangle, and is between the same parallels, then the parallelogram is double (the area) of the triangle.