Problem
GEO-B1-M06-P005 Diagonal of a Parallelogram
#5
★☆☆☆☆ Level 1 of 5
Prove that a diagonal of a parallelogram halves its area.
Compare the two triangles by the common diagonal and equal heights.
Let \(ABCD\) be a parallelogram. Diagonal \(AC\) divides it into triangles \(ABC\) and \(ACD\). They have common base \(AC\), and the heights from \(B\) and \(D\) to \(AC\) are equal because \(AB\parallel CD\). Hence these triangle areas are equal.
Connects parallelograms with the area method.