Please answer the foll:question
Consider a quadrilateral ABCD with mid points of AB,BC,CD and DA to be P,Q,R and S.
join the mid points to get quadrilateral PQRS.
Join diagonal AC of rectangle ABCD.
In triangle DAC,
SR parallel to AC and half of it( mid pt thm)
PQ parallel to AC and half of it
So PQRS is a parallelogram( one pair of oposite sides is parallel and equal)
Now to show that it's a rhombus,
we can eitther show that adjacent sides are equal or that the diagonals of PQRS bisect each other at 90 degrees.
We'll go for the first option.
We know that the angles of a rectangle are 90 degrees each.
So, using Pythagoras' them,
So we see that,
PQRS is a parallelogram with adjacent sides equal.
So PQRS must be a rhombus
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