Gallery Problems Exercise (Groups)

Dividing Parallelograms

Work Time

Dividing Parallelograms

Emma says that she can divide any parallelogram into four triangles with equal areas using this method:

  • On parallelogram ABCD, I draw diagonal AC.

  • Next, I mark the midpoint of line segment BC, which is point E. I draw line segment AE.

  • Finally, I mark the midpoint of line segment CD, which is point F. I draw line segment AF.

  • For any parallelogram, these steps result in four triangles with equal areas.

Is Emma right?

State your decision and justify it mathematically—that is, if you think Emma’s method works for any parallelogram, show why it does.

If you think it does not, show why not.