In a ΔABC, D and E are points on the sides AB and AC respectively.AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.

Question

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

AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.

Answer 1

We have,

We have,
AB = 10.8cm, BD = 4.5cm, AC = 4.8 cm and AE = 2.8cm
∴ AD = AB – DB = 10.8 – 4.5
⇒ AD = 6.3 cm
And, EC = AC – AE
= 4.8 – 2.8
⇒ EC = 2 cm

Thus, DE divides sides AB and AC of ΔABC in the same ratio. Therefore, by the converse of basic proportionality theorem.