Theorem 17 - A Diagonal Bisects the Area of a Parallelogram
This demonstrates that a diagonal of a parallelogram always splits the parallelogram into two triangles of equal area.
Change the shape of the parallelogram by dragging A, B, or D. Notice that the two triangles always have equal area. Are the triangles congruent? Are all triangles of equal area congruent? The diagonal [BD] will also split the parallelogram into two triangles of equal area. Are these triangles (ABD and CBD) congruent to ABC and ADC?