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In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR. - Mathematics

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In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

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Solution

In Δ POQ, AB || PQ

:.`(OA)/(AP) = (OB)/(BQ) `  (basic proportionality theorem)  (i)

In ΔPOR, AC||PR

`:.(OA)/(AP) = (OC)/(CR)`  (By basic proportionality theorem)  (ii)

From i and ii, we obtain

`(OB)/(BQ) = (OC)/(CR)`

`:. BC || OQ` (By Converse of basic proportionality theorem)

Concept: Similarity of Triangles
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APPEARS IN

NCERT Class 10 Maths
Chapter 6 Triangles
Exercise 6.2 | Q 6 | Page 129
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