A and B are respectively the points on the sides PQ and PR of a ∆PQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm, Is AB || QR? Give reason for your answer.

Question

Philoid · Accepted Answer

(True)

Given,

PQ = 12.5 cm,

PA = 5 cm,

BR = 6 cm and

PB = 4 cm

Then,

QA = QP – PA = 12.5 – 5 = 7.5 cm

Form Equations (i) and (ii).

PA/AQ = PB/BR

According to the converse of basic proportionality theorem, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Hence,

AB || QR.