Question

ABCD is a parallelogram. P,Q,R and S are the mid points of AB, BC, CD and DA respectively. Prove that the area of the parallelogram PQRS is equal to half the area of the parallelogram ABCD.
Please answer fast

Answer 1

Answer:

it is proved below

Step-by-step explanation:

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.

(i) In △DAC , S is the mid point of DA and R is the mid point of DC. Therefore, SR∥AC and SR=21AC.By mid-point theorem.

(ii) In △BAC , P is the mid point of AB and Q is the mid point of BC. Therefore, PQ∥AC and PQ=21AC.By mid-point theorem. But from (i) SR=21AC therefore PQ=SR

(iii)  PQ∥AC & SR∥AC therefore  PQ∥SR and PQ=SR. Hence, a quadrilateral with opposite sides equal and paralle is a parallelogram. Therefore PQRS is a parallelogram.