Question

In a ΔABC, D and E are points on the sides AB and AC respectively. For  the following case show that DE || BC

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

Answer 1

We have,

DE || BC

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

Now, ${\displaystyle \frac{\text{AD}}{\text{DB}}=\frac{5.7}{9.5}=\frac{57}{95}}$

${\displaystyle \Rightarrow \frac{\text{AD}}{\text{DB}}=\frac{3}{5}}$

And, ${\displaystyle \frac{\text{AE}}{\text{EC}}=\frac{3.3}{5.5}=\frac{33}{55}}$

${\displaystyle \Rightarrow \frac{\text{AE}}{\text{EC}}=\frac{3}{5}}$

Thus DE divides sides AB and AC of ΔABC in the same ratio.

Therefore, by the converse of basic proportionality theorem.

We have DE || BC