How many axes of symmetry has a equilateral triangle?

Answer 1

For an equilateral triangle, there are three axes of symmetry.

A plane figure is symmetrical about the line l if, whenever P is a point of the figure, so too is P', where P' is the mirror-image of P in the line l. The line is called a line of symmetry (or axis of symmetry), and the figure is said to be a symmetrical by the reflection in the line l.

An equilateral triangle with reflection symmetry has two halves that are mirror images of each other. If the shape is folded over its line of symmetry, the two halves of the shape match exactly. So, we can say that the two halves of an equilateral triangle are matched exactly only when its shape is folded over the lines of symmetry that passes through their vertixes and the midpoint of its sides. Thus, an equilateral triangle has three lines of symmetry, and three angles of rotation.

If you rotate any shape a full turn, it will look like it did before you rotated it. When you rotate a shape less than a full turn about its center point and it looks exactly as it did before you rotated it, it has rotation symmetry. In an equilateral triangle there are three places in the rotation where the triangle will look exactly the same as its starting position. If we turn the triangle one third of a full turn (60 degrees), the vertex 1 will be at position 3, vertex 2 will be at position 1, and vertex 3 will be at position 2, and the triangle will look like its starting position.