In a ΔABC, D and E are points on the sides AB and AC respectively. AB = 5.6cm, AD = 1.4cm, AC= 7.2 cm and AE = 1.8 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 = 5.6cm, AD = 1.4cm, AC= 7.2 cm and AE = 1.8 cm

Answer 1

We have, DE || BC

We have,
AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm
∴ DB = AB – AD
= 5.6 – 1.4
⇒ DB = 4.2 cm
And, EC = AC – AE
= 7.2 – 1.8
⇒ EC = 5.4 cm

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