Proof of Basics Proportionality Theorem (Thales Theorem) Theorem 6.1 : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Proof of Converse of Basic Proportionality Theorem Theorem 6.2 : If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

NCERT Exercise 6.2

Question 1. In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).