UPSC CDS Math Quadrilateral and Polygon Questions

Remember: In a triangle, the line segment joining the mid-points of any two sides of the triangle is parallel to the third side and half of it.
∴PQ=RS=

1

2

AC.....(1)
Also PQ|| RS || AC
Remember:In a quadrilateral, if one pair of opposite sides is parallel and equal, then it is a parallelogram.
Therefore, PQRS is a parallelogram.
SP=RQ=

1

2

BD....(2)
We know that the diagonals of a rectangle are equal.
∴ AC = BD.....(3)
From (1), (2) and (3), we have
PQ = QR = RS = SP
Therefore, parallelogram PQRS is a rhombus.