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 parallelogram and perimeter of PQRS = AC + BD . ​

Answer 1

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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.

Answer 2

Step-by-step explanation:

your answer

when I using parallelogram law

AB+AB2

area of a niche solvent from their respectively program AC + BD pqrs ABCD ABCD and address to the pqrs form a + b d