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Question
ΔABC and ΔDBC lie on the same side of BC, as shown in the figure. From a point P on BC, PQ||AB and PR||BD are drawn, meeting AC at Q and CD at R respectively. Prove that QR||AD.
Solution
In Δ CAB, PQ || AB.
Applying Thales' theorem, we get:
`(CP)/(PB)=(CQ)/(QA)` ...............(1)
Similarly, applying Thales theorem in BDC , Where PR||DM we get:
`(CP)/(PB)=(CR)/(RD)` ..................(2)
Hence, from (1) and (2), we have :
`(CQ)/(QA)=(CR)/(RD)`
Applying the converse of Thales’ theorem, we conclude that QR ‖ AD in Δ ADC. This completes the proof.
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