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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.

 


Solution

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)   
and PBBR=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.

Mathematics

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