Question

The quadrilateral formed by joining the mid-points of the side for quadilateral PQRS, taken in order, is a rhombus, if
A. PQRS is a rhombus
B. PQRS is parallelogram
C. diagonals of PQRS are perpendicular
D. diagonals of PQRS are equal

Answer 1

Correct Answer - D
Given, the quadrilateral ABCD is a rhombus.
So, sides AB, BC, CD and AD are equal.

Now, in `Delta`PQS, we have
D and C are the mid-points of PQ and PS.
So, `" "DC=(1)/(2)QS" "["by mid-point theorem"]...(i)` ltBrgt Similarly, in `Delta`PSR `" "BC=(1)/(2)PR" "["by mid-point theorem"]...(ii)`
As`" "BC=DC" "["since, ABCD is a rhombus"]` ltBrgt `therefore" "(1)/(2)QS=(1)/(2)PR" "["from Eqs. (i) and (ii)"]`
`rArr" "QS=PR`
Hence, diagonals of PQRS are equal.