Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus.

Explanation

Given : A rectangle ABCD in which P,Q,R and S are the mid-points of sides AB,BC,CD and DA respectively.

cons. : PQ,QR,RS and SP are joined and Join AC.

In `triangle` ABC,P and Q are the mid-points of sides AB and BC respectively.

`therefore` `PQ|\|AC` and `PQ=
1/2AC`___1 ( By mid point theorem)

In `triangle` ADC,R and S are the mid-points of sides CD and AD respectively.

`SR|\|AC` and `SR=1/2AC`_________2 ( By mid point theorem )

From 1 and 2

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