Question
Prove that through a given point, we can draw only one perpendicular to a given line. [Hint: Use proof by contradiction].
✓
Answer
From the point $P$, a perpendicular $PM$ is drawn to the given line $AB$. $\therefore\ \angle\text{PMB}=90^\circ$ Let if possible, we can draw another perpendicular $PN$ to the line $AB$. then, $\angle\text{PMB}=90^\circ$ $\angle\text{PMB}=\angle\text{PNB},$ which is possible only when $PM$ and $PN$ coincide with each other.
Hence, through a given point, we can draw only one perpendicular to a given line.
Hence, through a given point, we can draw only one perpendicular to a given line.
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