Diagonal of which type of quadrilaterals are congruent?

The diagonals of cyclic quadrilateral ABCD are congruent. Show that AD=BC and seg AB || seg CD.

Diagonal of which of the following quadrilaterals do not bisect it two congruent triangles ?

If the diagonals of a quadrilateral are congruent, then what type of quadrilateral is it ?

If two consecutive angles of cyclic quadrilateral are congruent, then prove that one pair of opposite sides is congruent and other is parallel.

If the diagonals of a cyclic quadrilateral intersect at the centre of a circle , then the quadrilateral is "_______________" .

Diagonals in the quadrilateral ABCD the line segments AC and BD are called its diagonals.

If the diagonals of a quadrilateral are perpendcular bisectors of each other, then what type of quadrilateral is it ?

If the diagonals of a quadrilateral are perpendcular bisectors of each other, then what type of quadrilateral is it ?