Q3 of 40 Page 8

In a ΔABC, lines are drawn through A, B and C parallel to sides BC, CA and AB respectively forming a triangle PQR. Prove that BC = QR.

BC ïï RQ, AB ïï QP and AC ïï RP
To Prove: BC = QR
Proof: Since QC ïï AB and QA ïï BC
... ABCQ is a parallelogram  (opposite sides are parallel)
... BC = AQ     ...... (opposite sides of parallelogram)....(i)
Similarly BCAR is a parallelogram and BC = AR ............(ii)
By adding (i) and (ii) 
we get
2BC = AQ + AR = QR
... BC = QR. 

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 4 ABCD is a parallelogram AB is produced to E so that BE = AB. Show that ED bisects BC.
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