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Question

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

CQ = QR

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D

None of the above

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Solution

The correct options are
A

PQ is parallel to AB


B

PQ = 12(AB - DC)


C

CQ = QR


By ASA Δ CDQ Δ RBQ
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=12 AR=12(ABRB)
=12(ABDC)[ RB=DC].


Mathematics

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