If in a parallelogram diagonals bisect each other at right angles and are equal, then it is a:
(i) A square
(ii) A rectangle
(iii) A rhombus

Verify your answer.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ taken in order is a square only if.
(i) $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is rhombus
(ii) Diagonals of $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ are equal.
(iii) Diagonals of $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ are equal and perpendicular.
(iv) Diagonals of $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ are perpendicular.

Verify your answer.