The adjoining figure shows a trapezium ABCD in which side AB is parallel to side DC. P and Q are mid - points of diagonals AC and BD respectively. CQ joined and produced meets AB at point R. Which of the following options are correct?
A
PQ is parallel to AB
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B
PQ = 12(AB - DC)
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C
Both (a) and (b)
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D
Neither (a) nor (b)
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Solution
The correct option is C Both (a) and (b) By ASA, ΔCDQ≡ΔRBQ ⇒ CQ = QR and DC = RB (i) In Δ ACR, P is mid-point of AC and Q is mid-point of RC ⇒ PQ || AR ⇒ PQ || AB (ii) In Δ ACR, P is mid-point of AC and Q is mid-point of CR ⇒PQ=12AR=12(AB−RB) =12(AB−DC)[∴RB=DC].