# 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.

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# Symmetry in an equilateral triangle. Theorem 1

# Axes of symmetry of an equilateral triangle

**Proof of the property of the axes of symmetry**

**Step 1**

**Step 2**

**Step 3**

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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

** **

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

** **

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

** **

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

Definition of an equilateral triangle

The criterion for a regular triangle

The area of an equilateral triangle. Formulas

The perimeter of an equilateral triangle

The angle bisector of a regular triangle. Properties

The height of a regular triangle. Properties

The median of a regular triangle. Properties

The property of the angles of an equilateral triangle

The exterior angle bisectors of an equilateral triangle

Similarity of regular triangle

The circle inscribed into an equilateral triangle. Properties

The circle circumscribed around a regular triangle. The theorems

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