Symmetry · Simetría
| English | Español |
|---|---|
| line symmetry/laɪn ˈsɪmətri/ | simetría lineal |
| mirror line/ˈmɪrə laɪn/ | eje de simetría |
| rotational symmetry/rəʊˈteɪʃənl ˈsɪmətri/ | simetría rotacional |
| order/ˈɔːdə/ | orden |
| plane of symmetry/pleɪn ɒv ˈsɪmətri/ | plano de simetría |
The snowflake test
- A snowflake has 6 lines of symmetry — fold it along any one and the halves match perfectly.
- Symmetry is nature's way of saying "this shape is balanced" — and mathematicians have a precise vocabulary for it.
Line symmetry 轴对称
- A shape has line symmetry (reflection symmetry) if a mirror line 对称轴 splits it into two matching halves.
- A square has 4 lines of symmetry: two diagonals and two through the midpoints of opposite sides.
- A nonsquare rectangle has 2 (only through midpoints); an equilateral triangle has 3.
Letter test. The letter "A" has 1 vertical line of symmetry. "H" has 2 (vertical and horizontal). "S" has 0 lines but has rotational symmetry 旋转对称.
Angles around a point add up to 360 degrees
Symmetry as a reflection · Simetría como reflexión
A shape has line symmetry if reflecting it leaves it unchanged. Reflect the shape and watch what is preserved. · Una figura tiene simetría axial si al reflejarla permanece inalterada. Refleja la figura y observa lo que se conserva.
How many lines of symmetry does a square have? · ¿Cuántas líneas de simetría tiene un cuadrado?
Two diagonals and two through the side midpoints: 4 lines. · Dos diagonales y dos por los puntos medios de los lados: 4 líneas.
Line symmetry means a mirror line splits the shape into: · La simetría axial significa que una línea de reflexión divide la figura en:
A line of symmetry reflects one half exactly onto the other. · Una línea de simetría refleja exactamente una mitad sobre la otra.
An equilateral triangle has ______ lines of symmetry. · Un triángulo equilátero tiene ______ líneas de simetría.
Each line goes from a vertex to the midpoint of the opposite side: 3 lines. · Cada línea va desde un vértice hasta el punto medio del lado opuesto: 3 líneas.
Rotational symmetry
- A shape has rotational symmetry if it fits onto itself as you turn it around its centre.
- The · El order · orden 阶 is how many times it fits in one full $360^{\circ}$ turn.
- A square has order $4$ (fits at $0^{\circ}$, $90^{\circ}$, $180^{\circ}$, $270^{\circ}$).
- A nonsquare rectangle has order $2$ (fits at $0^{\circ}$ and · y $180^{\circ}$).
Order 1 means no symmetry. Every shape fits itself after a full turn, so order 1 is not counted as rotational symmetry.
What is the order of rotational symmetry of a square? · ¿Cuál es el orden de simetría rotacional de un cuadrado?
A square fits onto itself 4 times in one full turn. · Un cuadrado coincide consigo mismo 4 veces en una vuelta completa.
What is the order of rotational symmetry of a rectangle (not a square)? · ¿Cuál es el orden de simetría rotacional de un rectángulo (no cuadrado)?
A rectangle fits itself at 0° and 180° — order 2. · Un rectángulo coincide consigo mismo a 0° y 180° — orden 2.
A shape with rotational symmetry of order 1 has rotational symmetry. · Una figura con simetría rotacional de orden 1 tiene simetría rotacional.
Order 1 means it only fits itself after a full turn — that is no rotational symmetry. · El orden 1 significa que solo coincide consigo mismo después de una vuelta completa, es decir, no tiene simetría rotacional.
Symmetry in 3D (Extended)
- A plane of symmetry 对称面 slices a solid into two mirror halves (like cutting an apple).
- An axis of symmetry is a line you can rotate the solid around so it fits itself.
- A cube has 9 planes of symmetry and · y 13 axes of symmetry.
Reflection in a mirror line produces a symmetric image — the basis of line symmetry.
You've got it
- line symmetry: a mirror line gives two matching halves
- rotational symmetry order = times it fits itself in one full turn
- a square: 4 lines of symmetry, rotational order 4