Question

In the given figure, $AO\times OB=OC\times OD$.


Which of the following is true?

• A. $△AOC\sim △DOB?$
• B. $△AOC\sim △BOD$
• C. $△COA\sim △DOB$
• D. None

Answer 1

The correct option is A $△AOC\sim △DOB?$

The given figure is as follows:


As $AO\times OB=OC\times OD$ (given)
$\Rightarrow \frac{AO}{DO}=\frac{OC}{OB}$
And,
$\angle AOC=\angle DOB$
(Vertically opposite angles)

Hence, $△AOC\sim △DOB$
(by SAS property)

SAS means two corresponding sides are proportional and the included angles are equal in measure.

So, option $\left(a\right)$ is correct.