Which letters have no symmetry

In mathematics, horizontal symmetry is less common than vertical symmetry. Horizontal symmetry can be observed in squares, rectangles, circles and ovals, though not in stars, triangles, hearts or pentagons.

Horizontal symmetry is also not encountered as often as vertical symmetry in everyday settings. That said, horizontal symmetry is somewhat common when applied to the alphabet. All of these words can be sliced in half horizontally to produce identical halves. There are multiple ways to identify the line of symmetry in an item, shape or object.

If the sides match up, you can identify that the shape has a line of symmetry; if they don't, you can determine that the shape is asymmetrical. You can also use a ruler to draw a straight line through the center of a shape horizontally or vertically and observe both sides to determine if there are identical traits. With three-dimensional objects, you can achieve a similar effect using a mirror to find a line of symmetry.

In the alphabet, over half of all letters have lines of symmetry. In total, 16 out of 26 letters are symmetrical along either their vertical or horizontal axes. Letters with horizontal symmetry are B, C, D and E. The letter O is special, as it is the only shape that boasts unlimited lines of symmetry. This means that it can be cut through the middle or folded in half in any direction and result in two identical halves, including diagonally known as diagonal lines of symmetry. For instance, the lowercase versions of the letters a, b, d and e all lose their lines of symmetry in lowercase.

Handwriting and font types can also impact lines of symmetry. For instance, certain fonts write the letter U with a small tail on the right side or the letter M with a top-left tail, while others write them with a smooth curve or uniform point. Letters with tails or embellishments may lose their lines of symmetry, while fonts that produce uniform letters retain them.

The star below has 5 lines of symmetry, five lines on which it can be folded so that both sides match perfectly. A common misconception found even in many glossaries and texts: Not all lines that divide a figure into two congruent parts are lines of symmetry.

For example, the diagonal of a non-square rectangle is not a line of symmetry. When a mirror is placed along the diagonal of a rectangle, the result does not look the same as the original rectangle, so the diagonal is not a line of symmetry. This new shape — the combination of the triangular half of the original rectangle and its image in the mirror — is called a kite.

Well before children begin any formal study of symmetry, playing with mirrors — perhaps on Pattern Block designs that they build — develops experience and intuition that can serve both their geometric thinking and their artistic ideas. The colorful design above has only vertical and horizontal lines of symmetry, but placing a mirror on it at another angle can create a beautiful new design.

More intrepid experiments give other interesting results. Note that some figures, like the star and the colorful blob at the top of the page, but not the letters N, Z, or S, have both reflective and rotational symmetry. A circle has infinitely many lines of symmetry: any diameter lies on a line of symmetry through the center of the circle.

Inspect them closely for any lines of symmetry. Which letters have zero lines of symmetry? Which letters have one line of symmetry?

Which letters have two lines of symmetry? Enter your answers below. The F and G have zero lines of symmetry. Those letters cannot be folded in half in any way with the parts matching up. Notice that the A has a vertical line of symmetry, while the B, C, D, and E have a horizontal line of symmetry. Let's look at some more letters! Think about whether any of these letters might have 2 lines of symmetry. J, K, L, N, and P have zero lines of symmetry.

M has one line of symmetry, and H, I, and O have 2 lines of symmetry. Did you get them all right? Do you see any lines of symmetry here? Right again! The Q, R, S are not symmetrical, so they have zero lines of symmetry. The T, U, and V are symmetrical, but they each have only one line of symmetry.