Split Parallelogram Area

PQRS is a parallelogram. Let m be a line that passes through the parallelogram in such a way that it splits the area into two equal parts. How many such lines can there be? If you were to draw all of these lines, you would notice something about them: What is it?


Show/Hide Solution

Draw the diagonals of parallelogram PQRS. Then draw any line (m) that passes through the intersection of the diagonals. Observe the three pairs of congruent triangles and observe that the area of the parallelogram has been bisected. Thus, any line m that passes through the intersection of the diagonals will also bisect the area of the parallelogram, providing an infinite number of possibilities.


Leave a Reply

Your email address will not be published.