Question

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.

Answer 1

In Δ POQ, AB || PQ

∴ `("OA")/("OP") = ("OB")/("OQ")`       ...(By basic proportionality theorem)     ...(i)

In ∆OPR, AC || PR

∴ `("OA")/("OP") = ("OC")/("OR")`       ...(By basic proportionality theorem)    ...(ii)

From (i) and (ii), we obtain

`("OB")/("OQ") = ("OC")/("OR")`

∴ `"BC" || "OQ"`            ...(By Converse of basic proportionality theorem)