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Show that the quadrilateral formed by jo...

Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus.

Text Solution

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Let ABCD be a rectangle and P, Q, R S be the midpoints of AB, BC, CD and DA respectively. We have shown earlier the PQRS is a ||gm.
Now, `triangle SAP ~= triangle QBP`
`[ because AS = BQ, angle A = angle B =90^(@) and AP=BP].`
`therefore PS=PQ.`
Hence, PQRS is a rhombus.
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