NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False Questions
Question 50

Question. 50

Two perpendiculars can be drawn to a given line from a point not lying on it.

Answer:

false

Detailed Answer with Explanation:

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.

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