Question

In the adjoining figure DE $\parallel$ BC and AD :DB =5 : 4, Find DE : BC,

Answer 1

In $△$s ADE and ABC,
$\angle DAE=\angle BAC$ (Common angle)
$\angle ADE=\angle ABC$ (Corresponding angles of parallel lines)
$\angle AED=\angle ACB$ (Corresponding angles of parallel lines)
Therefore, $△ADE\sim △ABC$ (AAA rule)
Hence, $\frac{AD}{AB}=\frac{DE}{BC}$
$\frac{AD}{AD+DB}=\frac{DE}{BC}$
$\frac{1}{1+\frac{DB}{AD}}=\frac{DE}{BC}$
$\frac{1}{1+\frac{4}{5}}=\frac{DE}{BC}$
$\frac{5}{9}=\frac{DE}{BC}$