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.

AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm and EC = 4 cm.

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

By Thale’s theorem,

Solving for ,

We need to find DB from given AB = 10.8 cm and AD = 6.3 cm.

DB = AB – AD

⇒ DB = 10.8 – 6.3

⇒ DB = 4.5

…(i)

Solving for ,

We need to find AE from given AC = 9.6 cm and EC = 4 cm.

AE = AC – EC

⇒ AE = 9.6 – 4

⇒ AE = 5.6

…(ii)

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

it satisfies Thale’s theorem.

Hence, we can say DE ∥ BC.