In a Δ ABC, D and E are points on the sides AB and AC respectively. S

1.	In a Δ ABC, D and E are points on the sides AB and AC respectively. Show that DE ∥ BC:If AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm, and AE = 2.8 cm.
Answer» We have AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm, and AE = 2.8 cm. So, AD = AB – DB = 10.8 – 4.5 = 6.3 And, CE = AC – AE = 4.8 – 2.8 = 2 It’s seen that, \(\frac{AD}{BD} = \frac{6.3}{4.5} = \frac{2.8}{2.0} = \frac{AE}{CE} = \frac{7}{5}\) So, by the converse of Thale’s Theorem We have, DE ∥ BC. Hence Proved.

In a Δ ABC, D and E are points on the sides AB and AC respectively. Show that DE ∥ BC:If AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm, and AE = 2.8 cm.

Answer»

We have

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

So,

AD = AB – DB = 10.8 – 4.5 = 6.3

And,

CE = AC – AE = 4.8 – 2.8 = 2

It’s seen that,

\(\frac{AD}{BD} = \frac{6.3}{4.5} = \frac{2.8}{2.0} = \frac{AE}{CE} = \frac{7}{5}\)

So, by the converse of Thale’s Theorem

We have,

DE ∥ BC.

Hence Proved.