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

Question 62

62. Is there any line of symmetry in the Fig. 9.12? If yes, draw all the lines of symmetry.

Answer: Yes, there is one line of symmetry — the straight line through points A and C.

Very simple explanation

1. Find a natural middle. Look at the points A (top) and C (bottom). They sit one above the other.

   ( ext{Draw a straight line passing through } A ext{ and } C.)

2. Fold test (think in your head). Imagine folding the picture along line AC.

   ( ext{Left side} o ext{Right side})

   ( ext{Point } B longleftrightarrow ext{Point } D)

   The two halves match exactly after the fold.
3. Distance check (why it works). Points B and D are the same “sideways” distance from line AC.

   (mathrm{dist}(B, AC) = mathrm{dist}(D, AC))

   That’s why folding across AC makes them sit on each other.
4. No other line works. If you try a horizontal line or any slanted line (like along the sides), the two halves will not look the same after folding.

   ( ext{So, only the line } AC ext{ is a symmetry line.})

How to draw it on paper

• Place your ruler on point A and point C.
• Draw a neat straight line through them.
• Label this line as the line of symmetry.