Question

D and E are respectively the points on the sides AB and AC of a DABC such that AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm, show that DE || BC.

Answer 1

We have,

AB = 12 cm, AC = 18 m, AD = 8 cm and AE = 12 cm.

So, BD = AB - AD = (12 - 8) cm = 4 cm

CE = AC - AE = (18 12) cm = 6 cm

Thus, DE divides sides AB and AC of DABC in the same ratio. Therefore, by the conserve of basic proportionality theorem, we have DE||BC.