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.


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