vertical line symmetry: M, A, T, H, I
horizontal line symmetry: H, E, C
none: S
so, more than one line: H
horizontal line symmetry: H, E, C
none: S
so, more than one line: H
Line symmetry, also known as reflective symmetry, occurs when a shape or pattern can be divided into two equal halves that mirror each other. In the context of letters, line symmetry refers to whether a letter can be split into two equal halves along a vertical line, where each half appears as a mirror image of the other.
To find the number of letters in "MATHEMATICS" with more than one line symmetry, we can analyze each letter individually:
1. M: M has vertical line symmetry. When divided along a vertical line, each half is a mirror reflection of the other.
2. A: The letter A has a horizontal line of symmetry, but it does not have vertical line symmetry. It cannot be divided into two equal halves along a vertical line that mirror each other.
3. T: T has vertical line symmetry. Each half of the letter is a mirror image of the other when divided vertically.
4. H: H has neither vertical nor horizontal line symmetry. It cannot be divided into equal mirror halves in any direction.
5. E: The letter E has both vertical and horizontal line symmetries. When divided along a vertical line, each half is a mirror reflection of the other. The same applies when divided horizontally.
6. M: As mentioned earlier, M has vertical line symmetry. Each half is a mirror reflection of the other.
7. A: As mentioned earlier, the letter A does not have vertical line symmetry. It cannot be divided into two equal mirror halves along a vertical line.
8. T: As mentioned earlier, T has vertical line symmetry. Each half of the letter is a mirror image of the other when divided vertically.
9. I: I has vertical line symmetry. Both halves are identical when divided along a vertical line.
10. C: C does not have vertical line symmetry. It cannot be divided into two equal mirror halves along a vertical line.
11. S: S does not have vertical line symmetry either. It cannot be divided into two equal mirror halves along a vertical line.
Considering the analysis of each letter, there are a total of 5 letters in the word "MATHEMATICS" - M, T, E, I, and T - that have more than one line symmetry.