Diagonal & Area of Parallelogram
A diagonal of a parallelogram divides it into two triangles of equal area.
Parallelograms and Triangles Between Same Parallels
Two parallelograms or triangles, having same or equal bases and having their other vertices on a line parallel to their bases, are said to be on the same or equal bases and between the same parallels.
Parallelogram on the same base (or equal bases) and between the same parallels are equal in area.
Triangles, on the same base and between the same parallels, are equal in area. Triangles on the same or equal bases, having equal areas have their corresponding altitudes equal.