In a ΔABC, D and E are points on the sides AB and AC respectively. AB = 2cm, AD = 8cm, AE = 12 cm and AC = 18cm

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 = 2cm, AD = 8cm, AE = 12 cm and AC = 18cm

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

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