Question

ABCD is a quadrilateral . P ,Q ,R and S are the mid points of AB, BC, CD
and AD respectively . Prove that PQRS is a IIgram and perimeter of
PQRS = AC + BD

Write your answer in copy according to class 9 if u will do so your answer will be marked as brainless

Answer 1

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= 1/2 AC.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= 1/2 AC.By mid-point theorem. But from (i) SR= 1/2 AC 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.