Question

if the diagonal of llgm are equal then show it is rectangle

Answer 1

if diagonals are equal and bisect each other,then their half is also equal.
Consider intersection point of these diagonals as centre of circle and take radius as the half of diagonals.
Draw a circle and then the llgm will be a cyclic quadilateral.
In a cyclic quadilateral,the sum of opp. angles is 180°. therefore,the opp. angles are 90°(the opp. angles of quadilateral are equal).