General enunciation: We have to prove that a diagonal of a parallelogram divides it into two congruent triangles.
Particular enunciation: Let the diagonal of the parallelogram ABCD is BD. The diagonal BD divides the parallelogram into two triangles ABD and BCD.
We have to prove that ∆ABD ≅ ∆BCD
Proof: Since ABCD is a parallelogram and the opposite sides and angles of a parallelogram are equal.
∴ AB = CD, BC = AD
and ∠ABC = ∠ADC
In ∆ABD and ∆BCD
AB = CD, BC = AD
and included ∠ABC = included ∠ADC
∴ ∆ABD ≅ ∆BCD. [ side-angle-side] (Proved)