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Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is a
  • a)
    Rectangle with one side 4cm
  • b)
    Parallelogram with one side 4cm
  • c)
    Square with one side 4 cm
  • d)
    Rhombus with each side 4cm
Correct answer is option 'D'. Can you explain this answer?
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Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides...
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Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides...
We will use the mid-point theorem here. It states that the line segment joining the mid-points of any two sides of the triangle is parallel to the third side and is half of it. 

Let us join AC and BD. In △ABC,
P and Q are the mid-points of AB and BC respectively.
∴ PQ || AC and PQ = 1/2 AC (Mid-point theorem) ... (1)
Similarly, in △ADC,
SR || AC and SR = 1/2 AC (Mid-point theorem) ... (2)
Clearly, PQ || SR and PQ = SR [From equation (1) and (2)]
Since in quadrilateral PQRS, one pair of opposite sides are equal and parallel to each other, it is a parallelogram.
∴ PS || QR and PS = QR (Opposite sides of the parallelogram) ... (3)
In △BCD, Q and R are the mid-points of side BC and CD respectively.
∴ QR || BD and QR = 1/2 BD (Mid-point theorem) ... (4)
However, the diagonals of a rectangle are equal.
∴ AC = BD ... (5)
Thus, QR = 1/2 AC
Also, in △BAD
PS || BD and PS = 1/2 BD
Thus, QR = PS .... (6)
By using Equations (1), (2), (3), (4), and (5), we obtain
PQ = QR = SR = PS
Therefore, PQRS is a rhombus.
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Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is aa)Rectangle with one side 4cmb)Parallelogram with one side 4cmc)Square with one side 4 cmd)Rhombus with each side 4cmCorrect answer is option 'D'. Can you explain this answer?
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Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is aa)Rectangle with one side 4cmb)Parallelogram with one side 4cmc)Square with one side 4 cmd)Rhombus with each side 4cmCorrect answer is option 'D'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is aa)Rectangle with one side 4cmb)Parallelogram with one side 4cmc)Square with one side 4 cmd)Rhombus with each side 4cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is aa)Rectangle with one side 4cmb)Parallelogram with one side 4cmc)Square with one side 4 cmd)Rhombus with each side 4cmCorrect answer is option 'D'. Can you explain this answer?.
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