If θ is the angle between the diagonals of a parallelogram ABCD whose vertices are A(0, 2), B(2,-1), C(4,

Given points of the parallelogram are A(0, 2), B(2,-1), C(4, 0) and D(2, 3)

The slope of diagonal AC =

The slope of diagonal BD =

So diagonal BD is perpendicular to X-axis. Hence it is parallel to Y-axis.

Product of slope of two diagonals is equal to -1.

Hence proved.