Question

O and E are respectively the points and on the sides AB and AC of a \triangle ABC such that AB = 5.6cm AD = 1.4cm AC =7.2cm AE = 1.8 Show that DE || BC​

Answer 1

We have 

AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.

∴       BD=AB−AD=(5.6−1.4) cm = 4.2 cm

and ,

EC=AC−AE=(7.2−1.8)cm = 5.4cm

Now,    DBAD=4.21.4=31 and ECAE=5.41.8=31

⇒         DBAD=ECAE

Thus, DE divides sides AB and AC of △ABC in the same ratio.

Therefore, by the converse of Basic Proportionality Theorem, we have DE∣∣BC

Hope it helps:)