# ABCD is a rectangle and P,Q,R,S are mid-point of the sides AB,BC,CD and DA respectively . show that the quadrilateral PQRS is a rhombus.

2
by vibhu25

2015-10-16T08:32:34+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
When pq r and s are the mid point that means pq=rq=rs=spalso pq is parallel so it is a rhombus
2015-10-16T10:39:25+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Consider triangles PBQ,  QCR,  RDS,  and  SAP :
AP = PB = CR = RD        They are all parallel to each other
BC = CD = DS = SA            they are parallel to each other.

angle PBQ = angle QCR = angle RDS = angle SAP = 90 deg.

So all the four triangles are congruent.  So PQ = QR = RS = SP

we know that QS   and  PR  are perpendicular to each other, as they are parallel to AB and BC respectively.

hence, PQRS is a Rhombus.