Question
Sun September 20, 2009 By: Ashutosh Pandey

Plz answer

Expert Reply
Fri October 23, 2009

join BD. consider triangle ABD.

P and S are the mid points of the sides of the triangle so line joining them is parallel to the third side BD  and half of it...(mid pt thm)

similarly,

QR is parallel to BD and half of it.

 so PQRS is a parallelogram...9one pair of opp sides is paralel and equal)

next

in triangle APS,

PS^2=SA^2+AP^2...Pythagoras thm

in tringle BPQ,

PQ^2=PB^2+BQ^2.. Pythagoras thm

but AP=PB..   P is mid pt given

and

AS=BQ (since AD=BC)

so PS=PQ...

Thus we have a parallelogram PQRS where one pair of adjacent sides is equal, hence it's a rhombus.

Home Work Help