CBSE Class 9 Answered

Let ABCD is quadrilateral .

A = C =

B = D = β

sum of all four abgles = 2 (α + β ) = 360

Hence (α + β ) = 180

If lines AD and BC are intersected by line AB and sum of interior angles A and B is 180  ( (α + β ) = 180 ) ,

then AD || BC .

Similarly , If lines AB and CD are intersected by line AD and sum of interior angles A and D is 180  ( (α + β ) = 180 ) ,

then AB || CD .

Opposite sides are parallel to each other in quadrilateral ABCD if opposite angles are equal .

Hence ABCD is parallelogram .