Q. 53.8( 9 Votes )

The quadrilateral A. PQRS is a rhombus

B. PQRS is a parallelogram

C. diagonals of PQRS are perpendicular

D. diagonals of PQRS are equal.

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.


ABCD is a rhombus


AB = BC = CD = DA


Now,


D and C are midpoints of PQ and PS


DC = 1/2QS [By midpoint theorem]


Also,


B and C are midpoints of SR and PS


BC = 1/2PR [By midpoint theorem]


ABCD is a rhombus


BC = CD


1/2QS = 1/2PR


QS = PR


Hence, diagonals of PQRS are equal

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