Question

if the non parallel sides of a Trapezium are equal, prove that it is cyclic

Answer 1

If the non parallel sides are equal then it is a isosceles trapezium.

Isosceles trapezium has the property that the adjacent angles of I.T.P. are equal.

Then, in trapezium ABCD
A+B+C+D=360
A+A+C+C=360(I.T.P.)
2A+2C=360
2(A+C)=360
A+C=360/2
A+C=180

If one pair of opposite angles are of 180, then it is cyclic.

Answer 2

draw a line from point A name E on CD
then triangle ADE is a isosceles triangle
then let angle B be 1
angle AEC be 2
and angle D be 3
and angle AED be 4
then 2+3 =180(linear pair)
then as 2=1 & 3=4
therefore 1+4=180
hence proved