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

Question 63

Explanation (Very Simple Steps)

Goal: We have a rectangle PQRS. We must tell which lines are its lines of symmetry.

1. What is a line of symmetry?
   If you fold a shape along this line, both halves match exactly.

   ( ext{Line of symmetry} Rightarrow ext{two identical halves on folding})

2. Look at the picture. Points A, B, C, D are the midpoints of the sides of the rectangle (as shown in the figure).

   (A, C ext{ are midpoints on opposite sides})

   (B, D ext{ are midpoints on the other pair of opposite sides})

3. First line of symmetry: Join the midpoints on the left and right sides.

   ( ext{Draw the line } AC)

   ( ext{This is a vertical line through the center})

   Folding the rectangle along AC makes the left half sit exactly on the right half.

4. Second line of symmetry: Join the midpoints on the top and bottom sides.

   ( ext{Draw the line } BD)

   ( ext{This is a horizontal line through the center})

   Folding the rectangle along BD makes the top half sit exactly on the bottom half.

5. Important check (diagonals): Are the diagonals lines of symmetry?

   ( ext{In a general rectangle: diagonals are NOT lines of symmetry})

   ( ext{Diagonals become symmetry lines only if it is a square})

Conclusion / Final Answer: