Question

In $\Delta ABC$, DE || BC. Then which of the following is stated by Basic Proportionality Theorem?

• A. $\frac{AD}{DB}=\frac{AE}{EC}$
• B. $\frac{AB}{DB}=\frac{AE}{EC}$
• C. $\frac{AD}{DB}=\frac{AC}{EC}$
• D. $\frac{AB}{DB}=\frac{EC}{AC}$

Answer 1

The correct option is A $\frac{AD}{DB}=\frac{AE}{EC}$

Basic Proportionality Theorem says that if DE || BC, the ratio in which point D divides AB is the same as the ratio in which point E divides AC.

The ratio in which D divides AB is given by $\frac{AD}{DB}$. Similarly, the ratio in which E divides AC is given by $\frac{AE}{EC}$.
$\Rightarrow \frac{AD}{DB}=\frac{AE}{EC}$