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

Given, AB || PQ and AC||PR

Need to prove BC || QR

⇒ In ΔOPQ, AB || PQ

⇒ Since, line drawn parallel to one side of triangle, intersects the other two sided in distinct point, then it divides the other 2 sides in same ratio.

⇒ ……………eq(1)

⇒ In OPR, AC || PR

⇒ ……………eq(2)

From eq(1) and (2)

⇒

Thus in OQR,

⇒ Line BC divides the triangle OQR in the same ratio

⇒ We know that if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

∴ BC || QR

Hence proved.