Question

P, Q, R and S are points of trisection of the sides AB, BC, CD and DA of a quadrilateral ABCD. What is PQRS?

• A. A parallelogram
• B. A rhombus
• C. A trapezium
• D. A square

Answer 1

Answer: (A)

A parallelogram

In triangle ABD, using the identity that if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

$PQ||BD$

Also, in triangle BCD,

$RS||BD$

$\Rightarrow PQ||RS$

Similarly, we can prove that $RQ||PS$

$\Rightarrow PQRS is a parallelogram