Question

$\text{If}BC||EF\text{and}FG||CD\text{then,}\frac{AE}{AB}=$ _____.

• A. $\frac{AG}{GD}$
• B. $\frac{GD}{AG}$
• C. $\frac{AG}{AD}$
• D. $\frac{CF}{AF}$

Answer 1

The correct option is C

$\frac{AG}{AD}$

$\text{In}\Delta ABC,$

$EF\parallel BC$

$\therefore \frac{AE}{AB}=\frac{AF}{AC}....\left(1\right)\text{(Basic proportionality theorem)}$

$\text{In}\Delta ACD,$

$FG\parallel CD$

$\therefore \frac{AF}{AC}=\frac{AG}{AD}....\left(2\right)\text{(Basic proportionality theorem)}$

$\text{From 1 \& 2,}$

$\frac{AE}{AB}=\frac{AF}{AC}=\frac{AG}{AD}$

$\Rightarrow \frac{AE}{AB}=\frac{AG}{AD}$