A diagonal of a parallelogram, divides it into two congruent triangles.

Given: A parallelogram ABCD and AC is a diagonal, the diagonal AC divides parallelogram ABCD into two triangles △ ABC and △ CDA.

To prove: These triangles △ ABD and △CDA are congruent,
                        △ ABC ≅ △ CDA

Proof: In △ ABC and △ CDA

BC ∥ AD and AC is a transversal.

So, ∠BCA = ∠DAC (pair of alternate angles)

Similarly, AB ∥ DC and AC is a transversal.

So, ∠BAC = ∠DCA (pair of alternate angles)

and AC = CA (Common)

So, △ ABC ≅ △CDA (By ASA rule)

or diagonal AC divides parallelogram ABCD into two congruent triangles △ ABC and △ CDA.                             

Hence proved.