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The quadrilateral formed by joining the mid-points of the sides of a quadrilateralPQRS, taken in order, is a rhombus, if(A) PQRS is a rhombus(B) PQRS is a parallelogram(C) diagonals of PQRS are perpendicular(D) diagonals of PQRS are equal. |
Answer» (D) diagonals of PQRS are equal. Explanation: Since, ABCD is a rhombus We have, AB = BC = CD = DA Now, Since, D and C are midpoints of PQ and PS By midpoint theorem, We have, DC = ½ QS Also, Since, B and C are midpoints of SR and PS By midpoint theorem We have, BC = ½ PR Now, again, ABCD is a rhombus ∴ BC = CD ⇒ ½ QS = ½ PR ⇒ QS = PR Hence, diagonals of PQRS are equal Therefore, option (D) is the correct answer. |
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