Q. 93.6( 10 Votes )

The figure obtain A. a rhombus

B. a rectangle

C. a square

D. any parallelogram

Answer :

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.


Join AC, RP and SQ


In ∆ABC,


P is midpoint of AB and Q is midpoint of BC


By midpoint theorem,


PQ AC and PQ = 1/2AC …(1)


Similarly,


In ∆DAC,


S is midpoint of AD and R is midpoint of CD


By midpoint theorem,


SR AC and SR = 1/2AC …(2)


From (1) and (2),


PQ SR and PQ = SR


PQRS is a parallelogram


ABQS is a parallelogram


AB = SQ


PBCR is a parallelogram


BC = PR


AB = PR [ BC = AB, sides of rhombus]


SQ = PR


diagonals of the parallelogram are equal


Hence, it is a rectangle.

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