The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rectangle, if
Question:
The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rectangle, if
(a) ABCD is a Parallelogram
(b) ABCD is rectangle
(c) diagonals of ABCD are equal
(d) diagonals of ABCD are perpendicular to each other.
Solution:
Since,
The quadrilateral formed by joining the mid-points of the sides of a parallelogram is parallelogram ,
The quadrilateral formed by joining the mid-points of the sides of a rectangle is rhombus,
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral with diagonals equal is rhombus, and
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral with diagonals perpendicular to each other is rectangle.
Hence, the correct option is (d).