Question

in the figure A,B and Care points on OP OQ and OR respectively such that AB||PQ and AC||PR show that BC||QR

Answer 1

AP/AO=OB/BQ (∵, AB||PQ).............(i)
AP/AO=OC/CQ (∵, AC||PR).............(ii)
FROM (i) and (ii)
OB/BQ = OC/CQ
THEREFORE, BC||QR (∵, CONVERSE OF BPT)

Answer 2

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Given here,

In ΔOPQ, AB || PQ

By using Basic Proportionality Theorem,

OA/AP = OB/BQ…………….(i)

Also given,

In ΔOPR, AC || PR

By using Basic Proportionality Theorem

∴ OA/AP = OC/CR……………(ii)

From equation (i) and (ii), we get,

OB/BQ = OC/CR

Therefore, by converse of Basic Proportionality Theorem,

In ΔOQR, BC || QR.