. ...

IN the fig. ABCD is a quadrilateral ...

Given - angle A = angle C ---1

and angle B = angle D --- 2

Adiing equations 1 and 2, 1+2,

we get

angle A + angle B = angle C+ angle D --- 3

We have

angle A + angle B + angle C+ angle D = 360^{o} (angle sum property of a quadrilateral)

FRom 3 v hve, angle A + angle B = angle C+ angle D

therfore

angle A + angle B + angle A + angle B = 360^{o}

2(angle A + angle B) = 360^{o}

angle A + angle B = 360^{o}/ 2

angle A + angle B = 180^{o} ^{ }-- 4

angle C = angle D =180^{o} ^{ }---5

From 4.. AD II BC (since <A nd <B r cointerior angles of the quadrilateral... if the sum of cointerior angles r supplementary thn the sides r parallel to each odr)

Similarly frm 5 AB II CD

**Hence ABCD is a parallelogram...**

100% users found this answer helpful.