Question

If the non parallel sides of a trapezium are equal, prove that it is cyclic


please answer fast​

Answer 1

draw CE parallel to DA

thereby AECB is parallelogram

so angle 1=2 and angle 3=4( opp. angles of a parallelogram are equal)

also, AD=CE (opp. sides of a llgm)

AD=BC( given) that is CE = BC

angle5=6(angles opp. to equal sides)

angle 4+5=180( linear pair)

angle 3+6=180

thus ABCD is a trapezium with angle B+D=180

therefore abcd is a cyclic quadrilateral

draw the diagram accordingly