Theorem 6.2 - If line divides any two sides of triangle in the same ratio, then the line is paralle to third side.jpg

2 Theorem 6.2 - Thus E and E Hence DE BC.jpg

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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Theorem 6.2 :- If line a divides any two side of a triangle in the same ratio, then the line is parallel to third side. Given :- Δ ABC and a line DE intersecting AB at D and AC at E, such that AD ﷮DB﷯ = AE ﷮EC ﷯ To Prove :- DE ∥ BC Construction :- Draw DE’ parallel to BC. Proof :- Since DE’ ∥ BC , By Theorem 6.1 :If a line is drawn parallel to one side of a triangle to intersecting other two sides not distinct points, the other two sided are divided in the same ratio. ∴ AD﷮DB﷯ = AE′﷮E′C﷯ And given that, AD﷮DB﷯ = AE﷮EC﷯ From (1) and (2) AE﷮EC﷯ = AE′﷮E′C﷯ Adding 1 on both sides AE﷮EC﷯ + 1 = AE′﷮E′C﷯ + 1 AE + EC﷮EC﷯ = AE′ + E′C﷮E′C﷯ AC﷮EC﷯ = AC﷮E′C﷯ EC = E’C Thus, E and E’ coincides. Hence DE ∥ BC.

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Davneet Singh
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