Question

ABCD is a rectangle. P, Q, R and S are the mid points AB,BC,CD and AD respectively. Prove that PQRS is a rhombus

Answer 1

ABCD is a rectangle P,Q,R,S are the mid point of rectangle.
AB || DC AND AD ||BC so ABCD is parallelograms .
p is mid point of AB and R is a mid point of DC so AP is parallel to DR so,, APRD is a parallelograms .
S is a mid point of AD and O is mid Point of PR
then AS is parallel to PO.
ASOP and is also a parallelograms and AP is = SO.

so ASOP is a rectangle then angle POS is of 90

hence in quadrilateral PQRS is a rhombus because it is a property of rhombus that diagonals of a rhombus bisect at right angle

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