Question

D and E are respectively the points on the sides AB and AC of a $\Delta ABC$ such that AB = 5.6 cm. AD = 1.4 cm. AC = 7.2 cm and AE = 1.8 cm. Show that $DE\parallel BC$.

Answer 1

Solution:

We have,

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

Now, $\frac{AD}{DB}=\frac{1.4}{5.6}=\frac{1}{4}$

$\frac{AE}{EC}=\frac{1.8}{7.2}=\frac{1}{4}$

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

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

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

$DE\parallel BC$