Question
Which of the following letters has a rotational symmetry but no line symmetry?
The correct answer is
Z
Letter Symmetry Analysis
Line symmetry is present when a shape can be folded along a line, making both halves identical mirror images.
Rotational symmetry is present when a shape looks the same after being rotated around a central point by less than a full turn ($360^\circ$).
Analyzing Each Letter's Symmetry
Let's examine the symmetry for each letter option:
- M: Has one vertical line of symmetry. It lacks rotational symmetry (except for a $360^\circ$ rotation).
- O: Possesses multiple lines of symmetry (vertical, horizontal). It has rotational symmetry, specifically order 2 (looks the same after a $180^\circ$ rotation).
- Z: Has no lines of symmetry. It does have rotational symmetry of order 2 (looks the same after a $180^\circ$ rotation).
- X: Has two diagonal lines of symmetry. It also has rotational symmetry of order 2 (looks the same after a $180^\circ$ rotation).
Symmetry Comparison Table
| Letter | Line Symmetry | Rotational Symmetry ($< 360^\circ$) |
|---|---|---|
| M | Yes (1 vertical line) | No |
| O | Yes (multiple lines) | Yes (order 2, $180^\circ$) |
| Z | No | Yes (order 2, $180^\circ$) |
| X | Yes (2 diagonal lines) | Yes (order 2, $180^\circ$) |
Conclusion on Letter Symmetry
The letter Z matches the criteria of having rotational symmetry but no line symmetry.
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Important Questions from Symmetry and Reflection
Number of lines of symmetry in a square is -
The curve given by xy = 15 is symmetrical about what?
- Which of the following letters does not have rotational symmetry?
- Nitu is always confused in identifying the transformations. Her mathematics teacher helped her by giving one simple word for each transformation namely : Reflection, Rotation, Translation and Enlargement.
Which of the following represents the correct sequence of meaning of each transformation as given above?
(1) Flip, Slide, Turn and Bigger Figure
(2) Turn, Slide, Flip and Bigger Figure
(3) Flip, Turn, Slide and Bigger Figure
(4) Slide, Flip, Turn and Bigger Figure - Which of the following has/have only two lines of symmetry?
A. Equilateral triangle
B. Rectangle
C. Rhombus
D. Isosceles triangle
Choose the correct option.
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