Question

In the given figure, DE $\parallel$ BC such that AE = $\left(1/4\right)$ AC. If AB = 6 cm, find AD.

Answer 1

Basic proportionality theorem: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.

As $DE\parallel BC$

$\angle ADE=\angle ABC$

$\angle AED=\angle ACB$

So by $AAA$ property,

$△ADE\sim △ABC$

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

Since it is given that $\frac{AE}{AC}=\frac{1}{4}$

We get, $\frac{AD}{6}=\frac{1}{4}$

$AD=1.5\text{cm}$

So, $AD=1.5\text{cm}$