Question
In Figure, if $PQ || RS$, prove that $\triangle POQ \sim \triangle SOR$.
✓
Answer
From the given figure we have,
$PQ || RS$ (Given)
So, $\angle$$P =$ $\angle$$S ($Alternate angles$)$
and $\angle$$Q =$ $\angle$$R ($Alternate angles$)$
Also, $\angle$$POQ =$ $\angle$$SOR ($Vertically opposite angles$)$
Therefore, $\triangle POQ \sim \triangle SOR$ $(AAA$ similarity criterion$)$
$PQ || RS$ (Given)
So, $\angle$$P =$ $\angle$$S ($Alternate angles$)$
and $\angle$$Q =$ $\angle$$R ($Alternate angles$)$
Also, $\angle$$POQ =$ $\angle$$SOR ($Vertically opposite angles$)$
Therefore, $\triangle POQ \sim \triangle SOR$ $(AAA$ similarity criterion$)$
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