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CBSE - X - Mathematics - Three Dimensional Geometry

Plz answer

Asked by Pandeyo 20th September 2009, 8:21 AM
Answered by Expert


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)


QR is parallel to BD and half of it.

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


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


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.

Answered by Expert 23rd October 2009, 9:01 AM

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