Question

D and E are respectively the points on the sides AB and AC of a $\Delta ABC$ such that AB = 4.8 cm. AD = 1.6 cm. AC = 4.2 cm and AE = 1.4 cm. Then prove that $DE\parallel BC$.

Answer 1

We have,

AB = 4.8 cm, AD = 1.6 cm, AC = 4.2 cm and AE = 1.4 cm.

Then DB = AB - AD = 4.8 - 1.6 = 3.2 cm
And EC = AC - AE = 4.2 - 1.4 = 2.8 cm

Now, $\frac{AD}{DB}=\frac{1.6}{3.2}=\frac{1}{2}$

$\frac{AE}{EC}=\frac{1.4}{2.8}=\frac{1}{2}$

$\Rightarrow \frac{AD}{DB}=\frac{AE}{EC}$

Thus, DE divides sides AB and AC of $\Delta ABC$ in the same ratio.

$\therefore$ By the converse of Basic Proportionality Theorem, we have
$DE\parallel BC$