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

Question 61

Why the statement is false

1. Know the shapes first.

   ( ext{A ray})

   starts at one point and goes on forever in one direction.

   ( ext{A line segment})

   has two endpoints and a fixed length.

2. What is a perpendicular bisector?

   It is a line that:

   • cuts a segment exactly at its midpoint, and
   • meets the segment at a right angle.

   (perp ext{ means “perpendicular”.})

   ( ext{Midpoint } M ext{ is the point halfway between the two endpoints.})

3. Key idea: The definition needs a segment (two endpoints) to have a midpoint.

   A ray has only one starting point and no second endpoint.

   So a ray has no midpoint.

4. Therefore: “Perpendicular bisector of a ray” is not defined, because there is nothing to bisect.

   You cannot draw even one perpendicular bisector of a ray, let alone infinitely many.

5. Extra clarity (about segments):

   If you take a specific segment, it has a unique perpendicular bisector.

   ( ext{Exactly one for each fixed segment.})

6. Conclusion: The statement “Infinitely many perpendicular bisectors can be drawn to a given ray” is

   (oxed{ ext{False}})