Question

In the given figure, OA = OC and AB = BC.

then,$\angle AOB={90}^{\circ }$

State whether the above statement is true or false.

• A. True
• B. False

Answer 1

Answer: (A)

In $△AOB$ and $△OBC$,

$OA=OC$ (Given)
$AB=BC$ (Given)
$OB=OB$ (common)

Thus, $△AOB\cong △COB$ (SSS rule)

Hence, $\angle AOB=\angle COB=x$ (By cpct)

We know, $\angle AOB+\angle COB=180$ (Angles on a straight line)

$x+x=180$

$x={90}^{\circ }$

Thus, $\angle AOB=\angle COB={90}^{\circ }$