Ex 6.2, 6
In figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.
Given:
AB II PQ and AC II PR
To prove: BC II QR
Proof:
In ∆ 𝑂𝑃𝑄
AB II PQ
(Line drawn parallel to one side of triangle, intersects the other two sides in distinct points, Then it divides the other 2 side in same ratio)
𝑂𝐴/𝐴𝑃=𝑂𝐵/𝐵𝑄
In ∆ 𝑂𝑃𝑅
AC II PR
(Line drawn parallel to one side of triangle, intersects the other two sides in distinct points, Then it divides the other 2 side in same ratio)
𝑂𝐶/𝐶𝑅=𝑂𝐴/𝐴𝑃
From (1) & (2)
𝑂𝐶/𝐶𝑅=𝑂𝐵/𝐵𝑄
Thus in Δ OQR,
𝑂𝐶/𝐶𝑅=𝑂𝐵/𝐵𝑄 i.e.
Line BC divides the triangle Δ OQR in the same ratio
∴ BC II QR
(If a line divides any two sides of a
triangles in the same ratio ,
then the line is parallel to the third side)
Hence proved

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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