Question

Question 3
A and B are respectively the points on the sides PQ and PR of a $\Delta$ 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.

Answer 1

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
$Now,\frac{PA}{AQ}=\frac{5}{7.5}=\frac{50}{75}=\frac{2}{3}...\left(i\right)$
$and\frac{PB}{BR}=\frac{4}{6}=\frac{2}{3}...\left(ii\right)$
From Eqs. (i) and (ii),
$\frac{PA}{AQ}=\frac{PB}{BR}$
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, $AB||QR$.