At some moment, two giant planets …

In Δ ABC, P and Q are the mid-points of sides AB and BC respectively. ∴ PQ || AC and PQ = 12 AC ( Using mid-point theorem) …..(1) In ΔADC, R and S are the mid - points of CD and AD respectively. ∴ RS || AC and RS = 12 AC ( Using mid-point theorem) …..(2) From equation (1) and (2) , we obtain PQ || RS and PQ = RS Since in quadrilateral PQRs, one pair of opposite sides is equal and parallel to each other , it is a parallelogram. Let the diagonals of rhombus ABCD intersect each other at point O. In Quadrilateral OMQN, MQ || ON (∵ PQ || AC) QN || OM (∵ QR || BD) Therefore, OMQN is a parallelogram. ∴∠MQN=∠NOM and ∠PQR=∠NOM However, ∠NOM=90∘ (Diagonals of a rhombus are perpendicular to each other) ∴∠PQR=90∘ Clearly , PQRS is a parallelogram having one of its interior angles as 90∘ Hence, PQRS is a rectangle.