D and E are points on the sides AB and AC respectively of a ΔABC. In each of the following cases, determine whether DE || BC or not.

AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm.

Here, by applying converse of Thale’s theorem we can conclude whether or not DE ∥ BC.

By Thale’s theorem,

Solving for ,

…(i)

Solving for ,

…(ii)

As equation (i) is equal to equation (ii),

it satisfies Thale’s theorem.

Hence, we can say DE ∥ BC.