Question

Prove that if three angles of a quadrilateral are equal, we say that quadrilateral is a parallelogram.

Answer 1

Given Thee angle of quadrilateral are equal

Then $\angle A=\angle B=\angle C$

But sum of angle of a quadrilateral=${360}^0$

If $\angle A=\angle C$ then AB||CD

$\therefore \angle A+\angle B+\angle C+\angle D={360}^0$

And $\angle D={360}^0-3\angle A$

$\therefore \angle D$ must be equal to $\angle A=\angle B=\angle C$

$\therefore AD||BC$

Then ABCD is a parallelogram