Question

ABCD is a rectangle formed by the points A (-1,-1), B(-1,4), C(5, 4) and D(5, -1). P, Q, R
and S are the mid-points of AB, BC, CD and DA respectively. What is the type of quadrilateral PQRS?
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Answer 1

Step-by-step explanation:

Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side

Therefore,

In Δ AOB, AB < OA + OB ……….(i)

In Δ BOC, BC < OB + OC ……….(ii)

In Δ COD, CD < OC + OD ……….(iii)

In Δ AOD, DA < OD + OA ……….(iv)

⇒ AB + BC + CD + DA < 2OA + 2OB + 2OC + 2OD

⇒ AB + BC + CD + DA < 2[(AO + OC) + (DO + OB)]

⇒ AB + BC + CD + DA < 2(AC + BD)

Hence, it is proved.