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Answer: The Contrary of Basic Proportionality Theorem is given as, “If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.”
The illustration can be made using the following example:
Consider a triangle ABC and a line intersecting AB in D and AC in E, such that AD / DB = AE / EC.
The claim that the lines DE being parallel to BC proves our theorem.
Assuming the contrary that, let DE be a line that is non-parallel to BC.
Clearly, there must be another line parallel to BC.
Let it be DF, such that it is parallel to BC.
This is possible only when F and E are same.
So, DF is the same as the line DE itself.
Therefore, DF is parallel to BC.
Hence the converse of BPT is proven.
