Question
Prove that the straight lines perpendicular to the same straight line are parallel to one another.
✓
Answer
Let $AB$ and $CD$ be drawn perpendicular to the Line $MN$ $\angle\text{ABD}=90^\circ$ $... (i)$
$[AB$ is perpendicular to $MN]$
$\angle\text{CON}=90^\circ$ $... (ii) [CD$ is perpendicular to $MN ]$
Now, $\angle\text{ABD}=\angle\text{CDN}=90^\circ$$[$From $(i)$ and $(ii)]$
Therefore,$ AB\ ||\ CD$, Since corresponding angles are equal.
$[AB$ is perpendicular to $MN]$
$\angle\text{CON}=90^\circ$ $... (ii) [CD$ is perpendicular to $MN ]$
Now, $\angle\text{ABD}=\angle\text{CDN}=90^\circ$$[$From $(i)$ and $(ii)]$
Therefore,$ AB\ ||\ CD$, Since corresponding angles are equal.
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