CBSE Class 10 Answered
Plz answer
Asked by Pandeyo | 20 Sep, 2009, 08:21: AM
Expert Answer
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.
Answered by | 23 Oct, 2009, 09:01: AM
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