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 = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm, and AE = 1.8 cm.
Answer» We have, AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm, and AE = 1.8 cm. So, BD = AB – AD = 5.6 – 1.4 = 4.2 cm And, CE = AC – AE = 7.2 – 1.8 = 5.4 cm It’s seen that, \(\frac{AD}{BD}\) = \(\frac{1.4}{4.2}\) = \(\frac{1}{3}\) \(\frac{AE}{CE}\) = \(\frac{1.8}{5.4}\) = \(\frac{1}{3}\) Thus, \(\frac{AD}{BD}\) = \(\frac{AE}{CE}\) 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 = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm, and AE = 1.8 cm.

Answer»

We have,

AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm, and AE = 1.8 cm.

So,

BD = AB – AD = 5.6 – 1.4 = 4.2 cm

And,

CE = AC – AE = 7.2 – 1.8 = 5.4 cm

It’s seen that,

\(\frac{AD}{BD}\) = \(\frac{1.4}{4.2}\) = \(\frac{1}{3}\)

\(\frac{AE}{CE}\) = \(\frac{1.8}{5.4}\) = \(\frac{1}{3}\)

Thus,

\(\frac{AD}{BD}\) = \(\frac{AE}{CE}\)

So, by the converse of Thale’s Theorem

We have,

DE ∥ BC.

Hence Proved.