Question
In Figure. $\triangle\text{ARO}\cong\triangle$ _________.
✓
Answer
In Figure. $\triangle\text{ARO}\cong\triangle\text{PQO}$ Solution: In $\triangle\text{ARO}$ and $\triangle\text{PQO},$ $\angle\text{AOR}=\angle\text{POQ}$ [vertically opposite angles] $\angle\text{ARO}=\angle\text{PQO}=55^{\circ}$ [given] $\Rightarrow \ \angle\text{RAO}=\angle\text{QPO}$ Now, in $\triangle\text{ARO}$ and $\triangle\text{PQO},$ $ \ \angle\text{AOR}=\angle\text{POQ}$ [vertically opposite angles] $\text{AO} = \text{PO} = 2.5\text{cm}$ $ \ \angle\text{RAO}=\angle\text{QPO}$ By Ass congruence criterion, $\triangle\text{ARO}\cong\triangle\text{PQO}$ [proved above]
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