Given: A parallelogram ABCD.
To Prove: A diagonal divides the parallelogram into two congruent triangles i.e., if diagonal AC is drawn then ∆ABC ≅ ∆CDA and if diagonal BD is drawn then ∆ABD ≅ ∆CDB
Construction: Join A and C
Proof: Sine, ABCD is a parallelogram AB ║ DC and AD ║ BC
In ∆ABC and ∆CDA
∠BAC = ∠DCA [Alternate angles]
∠BCA = ∠DAC [Alternate angles]
And, AC = AC [Common side]
∴ ∆ABC ≅ ∆CDA [By ASA]
Similarly, we can prove that
∆ABD ≅ ∆CDB
