Prove that the straight lines perpendicular to the same straight … - Vidyadip

Question

Prove that the straight lines perpendicular to the same straight line are parallel to one another.

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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.

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