Theorem 6.2 Converse of basic proportionality theorem (BPT) : If line a divides any two side of a triangle in the same ratio, then the line is parallel to third side Class 10

Given : In ΔABC, line DE intersects AB at D and AC at E,

To prove : DE || BC

Construction : Draw DE’ parallel to BC.

Proof : Assume that DE is not parallel to BC.

Let’s assume that DE’ is parallel to BC

from equation (1) & (2), we can see that E and E’ must coincide. 

Since DE’ || BC

therefore DE || BC.