Q. 103.9( 7 Votes )

# Show that t

Answer :

In ΔABC, P and Q are mid points of AB and BC respectively.

∴ PQ|| AC and PQ = 1/2AC … (1) …Mid point theorem

Similarly in ΔACD, R and S are mid points of sides CD and AD respectively.

∴ SR||AC and SR = 1/2AC …(2) …Mid point theorem

From (1) and (2), we get

PQ||SR and PQ = SR

Hence, PQRS is parallelogram ( pair of opposite sides is parallel and equal)

Now, RS || AC and QR || BD.

Also, AC ⊥ BD … as diagonals of rhombus are perpendicular bisectors of each other.

∴RS ⊥ QR.

Thus, PQRS is a rectangle.

Hence, the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rhombus is a rectangle.

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