State whether the given option is true or false.

The diagonal of a parallelogram divides it into two congruent triangles. 

The given statement is true.

A parallelogram's diagonals divide it into two congruent triangles.

Let us consider a parallelogram ABCD  with  AC as its diagonal.

To prove:  $∆ABC\cong ∆ADC$

Proof:

We know that the opposite sides of a parallelogram are parallel.

Hence, AB || DC and AD || BC, and AC is the transversal of the parallel lines AB and  DC

So, $\angle BAC=\angle DCA.......\left(1\right)$         [Alternative angles]

also, AC is the transversal of the parallel lines AD and  BC  

$\angle DAC=\angle BCA .....\left(2\right)$    [Alternative angles]

In $∆ABC$ and  $∆ADC$  

$\angle BAC=\angle DCA$ ,         (By equation 1)

 AC is the common side.

$\angle \mathrm{DAC}=\angle \mathrm{BCA}$ (By equation 2)

Therefore, $∆\mathrm{ABC}\cong ∆\mathrm{ADC}$.