Question

Question 6 In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Class 10 - Math - Triangles Page 129

Answer 1

∆OPQ s AB || PQ

.°. OA/AP = OB/BQ ( from formula )---(1)

∆OPR s AC || PR

.°. OA/AP = OC/CR ( from formula )-----(1)

from (1) and (2) we got

OB/BQ = OC/CR

.°. BC || QR

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Answer 2

In ΔOPQ, AB || PQ (Given)

∴ OA/AP = OB/BQ ...(i) [By using Basic Proportionality Theorem]


In ΔOPR, AC || PR (Given)

∴ OA/AP = OC/CR ...(ii) [By using Basic Proportionality Theorem]


From equation (i) and (ii), we get

OB/BQ = OC/CR


In ΔOQR, BC || QR. [By converse of Basic Proportionality Theorem]