The quadrilateral formed by joining the mid-points of the adjacent sides of a Quadrilateral $P Q R S$ , taken in order, is a rhombus, if
$P Q R S$ is a rhombus
$P Q R S$ is a parallelogram
diagonals of $P Q R S$ are equal.
diagonals of $P Q R S$ are perpendicular

Question

The quadrilateral formed by joining the mid-points of the adjacent sides of a Quadrilateral $P Q R S$ , taken in order, is a rhombus, if
$P Q R S$ is a rhombus
$P Q R S$ is a parallelogram
diagonals of $P Q R S$ are equal.
diagonals of $P Q R S$ are perpendicular

Toppr Admin · Accepted Answer

Diagonals of rectangle PQRS are equal -x21D2- In rhombus-the intersection of diagonals form 90o angles or right angles-This means they are perpendicular and they bisect each other in half-Therefore- diagonals are equal in length-

The quadrilateral formed by joining the mid-points of the adjacent sides of a Quadrilateral PQRS, taken in order, is a rhombus, ifPQRS is a rhombusPQRS is a parallelogramdiagonals of PQRS are equal.diagonals of PQRS are perpendicular

Diagonals of rectangle PQRS are equal :⇒ In rhombus,the intersection of diagonals form 90o angles or right angles.This means they are perpendicular and they bisect each other in half.Therefore, diagonals are equal in length.

The quadrilateral formed by joining the mid-points of the adjacent sides of a Quadrilateral $P Q R S$ , taken in order, is a rhombus, if
$P Q R S$ is a rhombus
$P Q R S$ is a parallelogram
diagonals of $P Q R S$ are equal.
diagonals of $P Q R S$ are perpendicular

Diagonals of rectangle PQRS are equal :
$\Rightarrow$ In rhombus,the intersection of diagonals form $90^{o}$ angles or right angles.
This means they are perpendicular and they bisect each other in half.
Therefore, diagonals are equal in length.