Question

In given figure, $\frac{OA}{OC}=\frac{OD}{OB}$. then prove that $\angle A=\angle C$ and $\angle B=\angle D$.

Answer 1

In ${△}^{\prime }sAOD$ and $COB$, we have

$\frac{OA}{OC}=\frac{OD}{OB}$

$\Rightarrow$ $\frac{OA}{OD}=\frac{OC}{OB}$

Also, $\angle 1=\angle 2$ [Vertically opposite angles]

So, by SAS-criterion of similarity, we have

$△AOD\sim △COB$

$\Rightarrow$ $\angle A=\angle C$ and $\angle B=\angle D$ $\left[Henceproved\right]$