The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD taken in order is a rectangle. What property does the quadrilateral ABCD possess?
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Given quadrilateral ABCD ,P,Q,R,S is the mid point of AB,BC,CD and
AC
Join AC
In triangle ABC pis the mid point of AB and Q is the mid point of BC
..PQ = AC and PQ||AC
.(1)
Similarly in triangle ADC, R is the mid point of CD and S is the mid point of AD
:.RS = ? AC and RS||AC
From equation (1) and (2), We get
RSIIPQ and RS=PQ So PQRS is a parallelogram (Because pair of opposite side of a quadrilateral is equal and parallel
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