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Question

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


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Solution

Given : PQ=12.5cm,PA=5cm,BR=6cm,PB=4cm

To prove : AB∥QR

We will solve it using Converse of Basic Proportionality Theorem .

Converse of Basic Proportionality Theorem : If a line segment intersecting two sides in two distinct points divides them in the same ratio then a line is parallel to the third side .

Proof : PQ=12.5cm,PA=5cm,BR=6cm,PB=4cm (given)

So QA=QP-PA=12.5-5=7.5cm

Now we find the ratio of

PAAQ=57.5=5075=23

Now we find the ratio of

PBBR=46=23

Here PAAQ=PBBR=23

So by using the converse of BPT we can say that AB∥QR .

Hence, AB∥QR.


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