A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively.
If quadrilateral ABCD is a rectangle, then the quadrilateral PQRS is
As ABCD is a rectangle, the diagonals AC and BD bisect each other and are equal in length.
By mid point theorem,
PS = QR = 12BD --------------------------- I
PQ = RS = 12AC ---------------------------- II
But, BD = AC
Therefore, PQ = QR = RS = PS => sides are equal.
So, PQRS is either a rhombus or a square.
Also, △AOB ≅ △SRQ
Thus, ∠AOB = ∠SRQ (by CPCTE)
We know that, diagonals of a rectangle do not intersect at 900.
Therefore, ∠SRQ ≠900
Hence, PQRS is a rhombus.