Question

Question 177
A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.

Answer 1

Consider a parallelogram ABCD.
Given, $\angle 1=\angle 2$
Since, ABCD is a parallelogram.
$AB\parallel CD$ and AC is the transversal.
$\therefore \angle 1=\angle 4$ [alternate angles] .... (i)
Similarly,
$\angle 2=\angle 3$ [alternate angles] .... (ii)
But given, $\angle 1=\angle 2$
$\therefore \angle 3=\angle 4$ [from Eqs. (i) and (ii)]

Yes, the diagonal will bisect the other angle.