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

Question

Philoid · Accepted Answer

Let there be a parallelogram ABCD and with one of its diagonal as AC.

Now, In ∆CDA and ∆ABC,

DA = BC (Opposite sides of parallelogram ABCD)

AC = AC (Common)

CD = AB (Opposite sides of parallelogram ABCD)

∴ By SSS axiom

∆CDA ≅ ∆ABC

ar(∆CDA) = ar(∆ABC) (by cpct)

Thus, we can say that the diagonal of a parallelogram divides it into two triangles of equal area.