Question 3 A and B are respectively the points on the sides PQ and PR of a Δ PQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm. Is AB||QR? Give reasons for your answer.
Proof : Given, AB is parallel to QR. Given that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm.
Then, QA = QP – PA = 12.5 – 5 = 7.5 cm Now,PAAQ=57.5=5075=23...(i) andPBBR=46=23...(ii) From Eqs. (i) and (ii), PAAQ=PBBR According to the basic proportionality theorem, if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio. Hence, by using the converse of basic proportionality theorem, AB||QR.