Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
This is Theorem 6.1 of Chapter 6 Class 10 in the NCERT Book.
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https://www.teachoo.com/4284/1051/Theorem-6.1---Basic-Proportionality-Theorem/category/Theorems/