Question

if the opposite angles of a quadrilateral are equal..prove that it is a parallelogram

Answer 1

Let ABCD  is a quadrilateral.

<A+<B+<C+<D = 360 ----(1)  [ Sum of the angles in a quadrilateral=360]

given <A =<C ----(2)

<B= <D----(3)
<A +<B +<A +<B =360 [using (2) and (3) in (1)]

2[<A+<B] =360

<A+<B =360/2

<A+<B =180 [ sum of the adjacent angles are supplementary in a quadrilateral then it is a parallelogram]

therefore
if the opposite angles of a quadrilateral are equal then it is a parallelogram