Question
In Figure, $\ce{AO = OB}$ and $\angle\text{A}=\angle\text{B}$.
$i.$ Is $\triangle\text{AOC}\cong\triangle\text{BOD}?$
$ii.$ State the matching pair you have used, which is not given in the question.
$iii.$ Is it true to say that $\angle\text{ACO}=\angle\text{BDO}?$

Answer

$i.$ Yes, by $\ce{ASA}, \triangle\text{AOC}\cong\triangle\text{BOD}$
$ii. \angle\text{OAC}=\angle\text{OBD}$ and $\ce{AO = OB}$
$iii.$ Yes, $\angle\text{AOC}=\angle\text{BOD} ($Opposite angles on same vertex$)$

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