All regular shapes have a line of symmetry. But you can get rid of its line of symmetry by making it irregular (so the angles aren't the same).
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The five shapes that have one line of symmetry are equilateral triangle, isosceles triangle, scalene triangle, rectangle, and rhombus. A shape has one line of symmetry if it can be folded along a line so that the two halves match exactly. In the case of these shapes, there is only one line that can divide the shape into two congruent halves.
Yes, they do exist. In fact, there are infinitely many of them.
Well, darling, shapes with only one line of symmetry are like the lone rangers of the symmetry world. We're talking about your squares, rectangles, and isosceles triangles strutting their stuff with just one line to keep them in check. So, if you're looking for a shape that's a bit of a rebel but still plays by the rules, these are the ones for you.
Shapes that can be divided into two equal parts are called "symmetrical" or "mirror image" shapes. When a shape can be divided into two equal halves that perfectly match each other, it is said to have reflectional symmetry. Examples of such shapes include squares, rectangles, circles, and triangles, as they can be divided into two equal parts along a line of symmetry.
A figure that has rotational symmetry but not line symmetry is a figure that can be rotated by a certain angle and still look the same, but cannot be reflected across a line to create a mirror image of itself. An example of such a figure is a regular pentagon, which has rotational symmetry of 72 degrees but does not have any lines of symmetry. This means that if you rotate a regular pentagon by 72 degrees, it will look the same, but you cannot reflect it across any line to create a mirror image.