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

Question 36

1. Mark the center.
   Imagine a point at the exact center of the hexagon.

2. Lines through opposite vertices.
   Join one vertex to the vertex directly opposite it (through the center). This is a symmetry line.
   There are 3 pairs of opposite vertices → 3 lines.

3. Lines through midpoints of opposite sides.
   Join the midpoint of one side to the midpoint of the side directly opposite it (through the center). This is also a symmetry line.
   There are 3 pairs of opposite sides → 3 lines.

4. Total lines of symmetry:

   ( ext{vertex–vertex lines} = 3 )

   ( ext{side–midpoint lines} = 3 )

   ( ext{total} = 3 + 3 = 6 )

General rule (for regular polygons):

( n = ) number of sides

( ext{lines of symmetry} = n )

For a regular hexagon, ( n = 6 ), so there are ( 6 ) lines of symmetry.