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Question 4
Prove that through a given point, we can draw only one perpendicular to a given line.

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Solution

Consider a line l and a point P.

Construction:
Draw two intersecting lines passing through the point P and which is perpendicular to l.
To prove: Only one perpendicular line can be drawn through a given point i.e., to prove P=0.
Proof:
In ΔAPB, A+P+B=180
[by angle sum property of a triangle]
90+P+90=180
P=180180
P=0
So, lines n and m coincide.
Hence, only one perpendicular line can be drawn through a give point.


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