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 β πππ
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)
ππ΄/π΄π=ππ΅/π΅π
In β πππ
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)
ππΆ/πΆπ =ππ΄/π΄π
From (1) & (2)
ππΆ/πΆπ =ππ΅/π΅π
Thus in Ξ OQR,
ππΆ/πΆπ =ππ΅/π΅π i.e.
Line BC divides the triangle Ξ OQR in the same ratio
β΄ 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

Article by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.