Question

Show that a diagonal divides a parallelogram into two triangles of equal area.

Answer 1

Let ABCD be a parallelogram and BD be its diagonal.
To prove: ar(∆ABD) = ar(∆CDB)

Proof:
In ∆ ABD and ∆CDB , we have:
AB = CD [Opposite sides of a parallelogram]
AD = CB [Opposite sides of a parallelogram]​

BD = DB [Common]

i.e., ∆ABD ≅ ∆CDB [ SSS criteria]
∴ ar(∆ABD) = ar(∆CDB)