Question

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.​

Answer 1

Answer:

Data: ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively.

To Prove: PQRS is a rhombus. Construction : Diagonals AC and BD are drawn.

Proof: In ∆ABC, P and Q are the mid-points of AD and BC.

∴ PQ || AC (Mid-point theorem)

PQ = 1 /2 AC (i)

Similarly, in ∆ADC, S and R are the mid-points of AD and CD.

∴ SR || AC SR = 1/2 AC (ii)

Similarly, in ∆ABD,

SP || BD SP = 1 /2 BD (iii)

Similarly, in ∆BCD, QR || BD QR = 1/ 2 BD

(iv) From (i), (ii), (iii) and (iv), PQ = QR = SR = PS and Opposite sides are parallel.

∴ PQRS is a rhombus.

Answer 2

Answer:

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Step-by-step explanation:

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