Question

(Converse of Thales' theorem) If a line divides any two sides of
a triangle in the same ratio then the line must be parallel to the
third side.



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Answer 1

Answer:

If a line is parallel to the third side then the line divides the other two lines in the same ratio

Answer 2

Answer:

Let DE is a line which is parallel tovBC

AD/BD=AE/EC-(given)-eq.1

it is supposed that DE is parallel BC

therefore AD/BD=AE/EC-eq.2 by (B.P.T)

therefore,from eq.1 and2

AE/EC=AE/AE/EC

This is not possible unless E' will concide with point E.

therefore,DE parallel BC.

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