Question

if a pair opposite sides of a cyclic quadrilateral are = .prove that its diagonals are equal

Answer 1

if the opposite angles are equal then it will be a parallelogram
we know that a cyclic parallelogram is rectangle

and in a rectangle the diagonls are equal

hope this helps!!!

Answer 2

since opposite sides equal
so this quadrilateral is parallelogram
since quadrilateral is cyclic
so sum of opposite angles is 180
since quadrilateral is parallelogram
so opposite angles equal
let abcd is quadrilateral
angle(a)+angle(c)=180
since opposite angles equal
so angle (a)+angle (a)=180
angle (a)=90
so each angle is 90
implies that abcd is rectangle
in which property diagonals equal
proved