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

Question 65

Step-by-step explanation (very simple)

Question: Write the letters of the word “MATHEMATICS” which have no line of symmetry.

1. What is a line of symmetry?

   ( ext{A line of symmetry divides a shape into two mirror halves.} )

   ( ext{If you fold on that line, both sides match exactly.} )

2. We will check each block capital letter in “MATHEMATICS” one by one.

   (Block style means simple straight lines and equal parts, like letters in maths diagrams.)

3. Test every letter:

   Letter	Has a line of symmetry?	Why (in simple words)
   M	Yes (vertical)	Left and right sides mirror each other.
   A	Yes (vertical)	Looks the same on both sides of the middle line.
   T	Yes (vertical)	Top bar is centered; left and right match.
   H	Yes (vertical and horizontal in block style)	Two upright bars with a middle bar—top/bottom and left/right match.
   E	Yes (horizontal)	Top and bottom arms match across a middle line.
   I	Yes (vertical and horizontal in block style)	Looks the same when folded left–right or top–bottom.
   C	Yes (horizontal in block style)	Top curve matches bottom curve across a middle line.
   S	No	Top and bottom are shaped differently; left and right are also different. No fold gives mirror halves.

4. Important note about repeated letters:

   In “MATHEMATICS”, some letters repeat (M, A, T). We only need to know whether that type of letter has symmetry or not.

5. Final check

   ( ext{M, A, T, H, E, I, C} \rightarrow ext{have at least one line of symmetry.} )

   ( ext{S} \rightarrow ext{has no line of symmetry.} )

Answer: S