Theorem 6.2 NCERT Class 10 Maths Chapter 6 Triangles

Theorem 6.2 NCERT Class 10 Maths Chapter 6 Triangles

Theorem 6.2:

If a line dives the two sides of the triangle in equal ratio, the line is parallel to the third side of the triangle.

if AD/DB = AE/EC, then DE ∥ BC.

Answer: This is converse of Theorem 6.1 which says a parallel line divides the sides of the triangle in equal ratio. We use that theorem to prove 6.2.

Let us assume that DE is not parallel, instead DE’ is parallel to BC.

So as per theorem 6.1,  AD/DB = AE’/E’C’. But in theorem 6.2 AD/DB = AE/EC. This is possible when E’ coincides with E. Hence we can say that line DE ∥ BC.

Next: Two triangles are similar if their corresponding angles are the same; AAA Similarity, Theorem 6.3.

See also: A line parallel to a side of the triangle divides the other sides in equal ratio; Theorem 6.1.

 

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