Question

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

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

Answer 1

AB = 12 cm, AD = 12 cm and AC = 18 cm.

∴ DB = AB – AD

= 12 – 8

⇒ DB = 4 cm

And, EC = AC – AE

= 18 – 12

⇒ EC = 6 cm

Now, `"AD"/"DB"=8/4=2/1`        [∵ DB = 4 cm]

And, `"AE"/"EC"=12/6=2/1`      [∵ EC = 6 cm]

`rArr"AD"/"DB"="AE"/"EC"`

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