The quadrilateral formed by joining the mid-points of the consecutive sides of a rectangle is a _____.

A rectangle ABCD in which P,Q, R and S are the mid-points of sides AB, BC, CD and DA respectively. PQ, QR, RS and SP are joined. 

Construction: Join AC. 

In ΔABC, P and Q are the mid-points of sides AB and BC respectively.
∴ PQ ∣∣ AC and PQ = $\frac{1}{2}$​AC   .....(i) (Mid pt. Theorem)
In ΔADC, R and S are the mid-points of sides CD and AD respectively.
∴ SR ∣∣ AC and SR = $\frac{1}{2}$​AC   ....(ii)  (Mid. pt. Theorem)
From (i) and (ii), we have
PQ ∣∣ SR and PQ = SR
⇒ PQRS is a parallelogram.
Now ABCD is a rectangle. 

∴ AD = BC

⇒$\frac{1}{2}$​AD = $\frac{1}{2}$​BC

⇒ AS = BQ   .....(iii)
In ΔAPS and ΔBPQ, we have
AP = BP   (P is the mid-point of AB)
∠PAS = ∠PBQ  (Each is equal to 90∘)
and AS = BQ  (From (iii))
∴ ΔAPQ ≅ ΔBPQ (SAS)
⇒ PS = PQ
∴ PQRS is a parallelogram whose adjacent sides are equal.
⇒PQRS is a rhombus.