In the given figure, if AB = BC and ∠BAO=∠BCO=90∘, then which of the fol

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In the given figure, if AB = BC and $∠ B A O = ∠ B C O = 90^{\circ}$ , then which of the following is true?

Options:

A .

△ A B O ≅ △ C B O

by RHS postulate

B .

△ A B O ≅ △ C B O

by ASA postulate

C . OA = OC

D . If

∠ A B O = 60^{\circ}

then,

∠ C B O = 60^{\circ}

Answer: Option A
:
A, C, and D

In $△ A B O$ and $△ C B O$

(i) $∠ B A O = ∠ C A O = 90^{\circ}$ ........ (given)

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

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

$\Rightarrow △ A B O ≅ △ C B O$ ........ (RHS Postulate)
$\Rightarrow$ OA = OC.......(cpct)
$\Rightarrow$ $∠ A B O = ∠ C B O = 60^{\circ}$ ........(cpct)

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