Question

Prove that if in a quadrilateral each pair of opposite Angles are equal then it is a parallelogram.

Answer 1

Suppose ABCD Is A Quadrilateral

Now As Given In The Question

Angle A = Angle C = x (lets say each be equal to x)

Angle B = Angle D = y (lets say each be equal to y)

Applying Angle Sum Property Of A Quadrilateral

A+B+C+D = 360

x+y+x+y = 360

2x+2y = 360

Dividing Both Sides By 2 will Yield

x+y = 180

But These Are Cointerior Angles

We Know that if cointerior angles are supplementary then the lines must be parallel.

Hence We Come To The Conclusion That AB Is Parallel To CD And AC Is Parallel To BD

If in a quadrilateral each pair of opposite sides is parallel then it is a parallelogram