Chapter 6 Class 10 Triangles

Class 10
Important Questions for Exam - Class 10

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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 πππ 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) ππ΄/π΄π=ππ΅/π΅π In β πππ 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) ππΆ/πΆπ=ππ΄/π΄π From (1) & (2) ππΆ/πΆπ=ππ΅/π΅π Thus in Ξ OQR, ππΆ/πΆπ=ππ΅/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