Let us draw the figure as per given condition (Fig.). In it, AC is a diagonal which bisects ∠BAD of the parallelogram ABCD, i.e., it is given that ∠BAC = ∠DAC. We need to prove that ∠BCA = ∠DCA.
AB || CD and AC is a transversal.
Therefore, ∠BAC = ∠DCA (Alternate angles) (1)
Similarly, ∠DAC = ∠BCA (From AD || BC) (2)
But it is given that ∠BAC = ∠DAC (3)
Therefore, from (1), (2) and (3), we have
∠BCA = ∠DCA