The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rectangle, if

Options

A. ABCD is a parallelogram
B. ABCD is a rectangle
C. diagonals of ABCD are equal
D. diagonals of ABCD are perpendicular to each other

Answer

B

Explanation

PQRS is always a parallelogram.
By midpoint theorem,
`PS||BD and PQ||AC `
`rArr LP||OM and PM||LO rArr LPMO " is a ||gm".`
`rArr angle LPM= angle LOM=90^(@) " "[because AC bot BD "(given)"].`
Now, PQRS is a ||gm with one angle `angle P=90^(@)` .
`therefore ` PQRS is a rectangle if AC `bot` BD. so ABCD is a rectangle