Question

In the given figure, ABCD is a trapezium in which
(i) AB || CD
(ii) $\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}$
(iii) AB = 5 cm

Find the value of CD . $\left[4\text{Marks}\right]$

Answer 1

Here, AB || CD (given)

$\Rightarrow \angle AOB=\angle COD$
($\because$ vertically opposite angles are equal)

$\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}$ (given)

$\therefore △AOB\sim △COD$ (by SAS similarity criterion) $\left[2\text{Marks}\right]$

$\Rightarrow \frac{AO}{OC}=\frac{OB}{OD}=\frac{AB}{CD}=\frac{1}{2}$
($\because$ corresponding sides of similar triangles will be in same ratio)

$\frac{AB}{CD}=\frac{1}{2}$

$\Rightarrow$ CD = 2 $\times$ AB = 2 $\times$ 5 = 10 cm $\left[2\text{Marks}\right]$