Question

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

(i) AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm.
(ii) AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 and AE = 1.8 cm.
(iii) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.
(iv) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm

Answer 1

(i) It is given that and are point on sides AB and AC.

We have to prove that DE || BC.

According to Thales theorem we have

(Proportional)

Hence, DE || BC.

(ii) It is given that and are point on sides AB and AC.

We have to prove that DE || BC.

According to Thales theorem we have

(Proportional)

Hence, DE || BC.

(iii) It is given that and are point on sides AB and AC.

We have to prove that DE || BC.

According to Thales theorem we have

So

$AD=AB-DB=10.8-4.5=6.3$

And

$EC=AC-AE=4.8-2.8=2$

Now

Hence, DE || BC.

(iv) It is given that and are point on sides AB and AC.

We have to prove that DE || BC.

According to Thales theorem we have

(Proportional)

Hence, DE || BC.