Question

In the figure, ABCD is a trapezium in which, AB || DC and $\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}andAB=5cm$. Find the value of CD .

(2 Marks)

Answer 1

In $\Delta AOB$ and $\Delta COD$,

$\angle AOB$ = $\angle COD$
(vertically opposite angles) (0.5 marks)

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

$\therefore △AOB\sim △COD$
(by SAS similarity criterion) (0.5 marks)

$\Rightarrow \frac{AO}{OC}=\frac{BO}{OD}=\frac{AB}{CD}=\frac{1}{2}$ (0.5 marks)

$\Rightarrow CD=2\times AB=2\times 5=10cm$ (0.5 marks)