# Axes of symmetry of an equilateral triangle

A regular triangle has three axes of symmetry. The axes of symmetry coincide with the angle bisectors, medians, heights and perpendicular bisectors. Axes of symmetry of an equilateral triangle

## Step 1

Consider equilateral triangle ABC (АВ=ВС=АС=а).

In this triangle, consider sides АВ=ВС. As the lengths of these sides are equal, then according to the property of an isosceles triangle: the angle bisector, the median, the height and the perpendicular bisector drawn from vertex B to base AC will be the axis of symmetry. Proof of the property of the axes of symmetry. Step 1

## Step 2

Consider sides АС=СВ. As the lengths of these sides are equal, then according to the property of an isosceles triangle: the angle bisector, the median, the height and the perpendicular bisector drawn from vertex C to base AB will be the axis of symmetry. Proof of the property of the axes of symmetry. Step 2

## Step 3

Consider sides СА=АВ. As the lengths of these sides are equal, then according to the property of an isosceles triangle: the angle bisector, the median, the height and the perpendicular bisector drawn from vertex A to base BC will be the axis of symmetry.

The property is proved. Proof of the property of the axes of symmetry. Step 3