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 = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC =10 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 = 12 cm and AD = 7.2 cm.

DB = AB – AD

⇒ DB = 12 – 7.2

⇒ DB = 4.8

…(i)

Solving for ,

We need to find EC from given AC = 10 cm and AE = 6.4 cm.

EC = AC – AE

⇒ EC = 10 – 6.4

⇒ EC = 3.6

…(ii)

As equation (i) is not equal to equation (ii),

it doesn’t satisfies Thale’s theorem.

Hence, we can say DE is not parallel to BC.