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 AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm, and EC = 5.5 cm.
Answer» We have AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm, and EC = 5.5 cm Now, \(\frac{AD}{BD} = \frac{5.7}{9.5} = \frac{3}{5 }\) And, \(\frac{AE}{CE} = \frac{3.3}{5.3} = \frac{3}{5 }\) 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 AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm, and EC = 5.5 cm.

Answer»

We have

AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm, and EC = 5.5 cm

Now,

\(\frac{AD}{BD} = \frac{5.7}{9.5} = \frac{3}{5 }\)

And,

\(\frac{AE}{CE} = \frac{3.3}{5.3} = \frac{3}{5 }\)

Thus,

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

So, by the converse of Thale’s Theorem

We have,

DE ∥ BC.

Hence Proved.