NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False Questions
Question 49

Question. 49

Only one perpendicular bisector can be drawn to a given line segment.

Answer:

true

Detailed Answer with Explanation:

What the words mean

A perpendicular bisector is a line that:

  • cuts a line segment exactly in the middle (at its midpoint), and
  • meets the segment at a right angle.

(90^circ)

Step-by-step idea

  1. Take a line segment.

    2. ( overline{AB} )

  2. Find its exact middle point.

    3. ( M ) is the midpoint of ( overline{AB} ).

  3. Draw a line through (M) that is at a right angle to the segment.

    4. ( ell perp overline{AB} ) at ( M ).

  4. This line ( ell ) is a perpendicular bisector because:
    • it passes through the midpoint ( M ) (so it bisects), and
    • it is perpendicular to ( overline{AB} ) (so it makes (90^circ)).

Why is there only one?

Through a fixed point on a line, there is only one line that can be drawn perpendicular to that line.

Through ( M ) to ( overline{AB} ), only one perpendicular exists.

If we assume there are two different perpendicular bisectors, then both would:

  • pass through the same midpoint ( M ), and
  • be perpendicular to the same segment ( overline{AB} ).

But two distinct lines cannot both be perpendicular to the same line at the same point ( M ).

So they would actually be the same line. Therefore, the perpendicular bisector is unique.

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 9: Symmetry and Practical Geometry – True or False Questions | Detailed Answers