Question

In Fig. 7.141 DE || BC such that $AE=\left(\frac{1}{4}\right)AC$. If AB = 6 cm, find AD.

Answer 1

In ABC and ADE
DAE = BAC (common angle)
ADE= ABC ( corresponding angles)
AED = ACB (corresponding angles)

Hence, ABC andAXY are similar by AAA criteria.
So,

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

$\Rightarrow$ $\frac{1}{4}=\frac{AD}{6}$

$\Rightarrow$ AD = $\frac{6}{4}$

$\Rightarrow$ AD = 1.5 cm