Question

In a ΔABC, D and E are points on the sides AB and AC respectively. For  the following case show that DE || BC

AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm.

Answer 1

We have,

DE || BC

We have, AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm

Now, `"AD"/"DB"=5.7/9.5=57/95`

`rArr"AD"/"DB"=3/5`

And, `"AE"/"EC"=3.3/5.5=33/55`

`rArr"AE"/"EC"=3/5`

Thus DE divides sides AB and AC of ΔABC in the same ratio.

Therefore, by the converse of basic proportionality theorem.

We have DE || BC