In the figure,if $PQ || RS,$ prove that $\Delta POQ \sim \Delta SOR$.
(N/A) Given: $PQ || RS$.
To prove: $\Delta POQ \sim \Delta SOR$.
Proof:
In $\Delta POQ$ and $\Delta SOR$:
$1$. $\angle P = \angle S$ (Alternate interior angles,as $PQ || RS$ and $PS$ is a transversal).
$2$. $\angle Q = \angle R$ (Alternate interior angles,as $PQ || RS$ and $QR$ is a transversal).
$3$. $\angle POQ = \angle SOR$ (Vertically opposite angles).
Therefore,by the $AAA$ (Angle-Angle-Angle) similarity criterion,$\Delta POQ \sim \Delta SOR$.
To prove: $\Delta POQ \sim \Delta SOR$.
Proof:
In $\Delta POQ$ and $\Delta SOR$:
$1$. $\angle P = \angle S$ (Alternate interior angles,as $PQ || RS$ and $PS$ is a transversal).
$2$. $\angle Q = \angle R$ (Alternate interior angles,as $PQ || RS$ and $QR$ is a transversal).
$3$. $\angle POQ = \angle SOR$ (Vertically opposite angles).
Therefore,by the $AAA$ (Angle-Angle-Angle) similarity criterion,$\Delta POQ \sim \Delta SOR$.
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