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.

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) [1 Mark]

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

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

$\Rightarrow CD=2\times AB=2\times 5=10cm$ [1 Mark]