NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Fill in the Blanks

Question 35

35. The line of symmetry of a line segment is the _____ bisector of the line segment.

Answer: perpendicular bisector.

Beginner-friendly Explanation (step by step)

1. Take a line segment with two endpoints. Let’s name them (A) and (B).

   ( ext{Segment } overline{AB})

2. Find the middle point of the segment. This point is called the midpoint, say (M).

   (M ext{ is halfway between } A ext{ and } B)

   (AM = MB)

3. Draw a new line that passes through the midpoint (M).

   (ell ext{ passes through } M)

4. Make sure this new line is at a right angle (90°) to the segment (overline{AB}).

   (ell perp overline{AB})

   (angle(ell, overline{AB}) = 90^circ)

5. This special line does two things:

   • It bisects the segment (cuts it into two equal parts at (M)).
   • It is perpendicular to the segment (meets it at a right angle).

6. Now, if you fold the segment along this line, point (A) lands exactly on point (B), and the two halves match perfectly.

   ( ext{Reflection across } ell: A leftrightarrow B)

7. Because folding (or reflecting) across this line makes the two sides match, this line is a line of symmetry for the segment.