NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False Questions

Question 50

Reason (very simple steps):

1. Draw a line l and take a point P that is not on the line.
2. From P, draw one line that makes a right angle with l.

   ( ext{Right angle} = 90^circ )

3. This line is called the perpendicular from P to l.
4. Now think: if you turn this line a little bit around point P, the angle with l will change.

   ( ext{Angle} < 90^circ )

   or

   ( ext{Angle} > 90^circ )

   It will no longer be a right angle.
5. So there is only one position of the line through P that makes

   ( 90^circ )

   with l. Any other line through P will not be perpendicular.

Conclusion: From a point outside a line, exactly one perpendicular can be drawn. Therefore, the statement “Two perpendiculars can be drawn…” is false.