Question

show that the quadrilateral formed by joining the midpoints of the side of a square is also a square

Answer 1

suppose ABCD is the square and pqrs is the quadrilateral formed after joining the points of sides of square now we join AC and BD as they become the diagonals of the square now according to mid point theorem PQ is parallel to BD and PQ is equals to half of BD similarly SR is parallel to BD and SR is equals to half of BD similarly s p and r q will be equal to half of AC

SP=RQ=1/2AC..............1
SR=PQ=1/2BD
diagonals os square are equal therefore AC = BD
THEREFORE SR=PQ=1/2AC.........2

from 1 and 2 SR=RQ=SP=PQ
Because all sides of the given quadrilateral are equal there for the given quadrilateral is a square

Answer 2

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