NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False QuestionsQuestion 49
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False Questions
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
- Take a line segment.
- Find its exact middle point.
- Draw a line through (M) that is at a right angle to the segment.
- 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)).
( overline{AB} )
( M ) is the midpoint of ( overline{AB} ).
( ell perp overline{AB} ) at ( M ).
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.