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 = 11.7 cm, AC = 11.2 cm, BD = 6.5 cm and AE = 4.2 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 AD from given AB = 11.7 cm and BD = 6.5 cm.

AD = AB – BD

⇒ AD = 11.7 – 6.5

⇒ AD = 5.2

…(i)

Solving for ,

We need to find EC from given AC = 11.2 cm and AE = 4.2 cm.

EC = AC – AE

⇒ EC = 11.2 – 4.2

⇒ EC = 7

…(ii)

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

it doesn’t satisfies Thale’s theorem.

Hence, we can say DE not parallel to BC.