Question

In the given figure, if AB = BC and $\angle BAO=\angle BCO={90}^{\circ }$, then which of the following is true?

• A. $△ABO\cong △CBO$ by RHS postulate
• B. $△ABO\cong △CBO$ by ASA postulate
• C. OA = OC
• D. If $\angle ABO={60}^{\circ }$ then, $\angle CBO={60}^{\circ }.$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $△ABO\cong △CBO$ by RHS postulate
C OA = OC
D If $\angle ABO={60}^{\circ }$ then, $\angle CBO={60}^{\circ }.$

In $△ABO$ and $△CBO$

(i) $\angle BAO=\angle BCO={90}^{\circ }$ ........ (given)

(ii) BO = BO .........(common side)

(iii) AB = BC........ (given)

$\Rightarrow △ABO\cong △CBO$ ........ (RHS Postulate)
$\Rightarrow$ OA = OC.......(cpct)
$\Rightarrow$ $\angle ABO=\angle CBO$ ........(cpct)

$\therefore$ If $\angle ABO={60}^{\circ }$ then, $\angle CBO={60}^{\circ }.$