NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Problems and Solutions

Question 67

Explanation (Step by Step)

What is a line of symmetry? It is a line that divides a shape into two equal mirror parts. If you fold the shape along this line, both sides match exactly.

1. Isosceles triangle — two equal sides and equal base angles. It has one vertical line that splits it into two same halves.

   ( ext{Lines of symmetry} = 1)

2. Square — all sides equal and all angles right angles. It has 4 symmetry lines: 2 through midpoints (horizontal & vertical) and 2 diagonals.

   ( ext{Lines of symmetry} = 4)

3. Kite — two pairs of equal adjacent sides. Only the line through the longer diagonal (joining the unequal angles) is a symmetry line.

   ( ext{Lines of symmetry} = 1)

4. Equilateral triangle — all sides and angles equal. Each vertex to the midpoint of the opposite side gives a symmetry line (3 in total).

   ( ext{Lines of symmetry} = 3)

5. Rectangle — opposite sides equal, all angles right angles. It has 2 symmetry lines through the midpoints: one horizontal and one vertical (diagonals are not symmetry lines unless it’s a square).

   ( ext{Lines of symmetry} = 2)

6. Regular hexagon — all sides and angles equal. Every vertex-to-opposite-vertex and midpoint-to-opposite-midpoint is a symmetry line (total 6).

   ( ext{Lines of symmetry} = 6)

7. Scalene triangle — all sides different. No fold makes two equal halves.

   ( ext{Lines of symmetry} = 0)

Now match each shape to its symmetry count

Final Answer: (i)→(f), (ii)→(c), (iii)→(f), (iv)→(d), (v)→(e), (vi)→(a), (vii)→(g)