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.

Оси симметрии равностороннего треугольника

Axes of symmetry of an equilateral triangle

Proof of the property of the axes of symmetry

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.

Оси симметрии равностороннего треугольника

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.

Оси симметрии равностороннего треугольника

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.

Оси симметрии равностороннего треугольника

Proof of the property of the axes of symmetry. Step 3