A diagonal of a parallelogram bisects one of its angle. Verify that it will bisect its opposite angle also.
Solution:
Let us draw the figure as per given condition.
It is given that \(∠BAC = ∠DAC\)
We need to prove that \(∠BCA = ∠DCA\).
\(AB ||\) and \(AC\) is a .
Therefore, \(∠BAC = ∠\) (Alternate angles) -----(1)
Similarly, \(∠DAC = ∠\) (From \(AD || BC\)) -----(2)
But it is given that \(∠BAC = ∠DAC\) ------(3)
Therefore, from (1), (2) and (3),
we have \(∠BCA = ∠DCA\)