# An equilateral triangle has the following property:

All angles of a regular triangle are equal to each other in length and are each 60 degrees.

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# The property of the angles of an equilateral triangle

# An equilateral triangle has the following property:

**Proof of the property of the angles**

** **

**Step 1**

**Step 2**

**Step 3**

**Step 4**

**Step 5**

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All angles of a regular triangle are equal to each other in length and are each 60 degrees.

The angles of an equilateral triangle

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Consider an equilateral triangle АВС (АВ=ВС=АС).

Prove that:

Proof of the property of the angles. Step 1

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As by condition АB=ВС, then the base BC angles are congruent:

Proof of the property of the angles. Step 2

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As by condition АС=ВС, then the base AB angles are congruent:

Proof of the property of the angles. Step 3

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As:

∠A=∠B and ∠B=∠C, then:

Proof of the property of the angles. Step 4

** **

As the sum of angles of a triangle equals 180 ⁰, then:

Since the three angles are congruent:

Therefore,

The property is proved.

Proof of the property of the angles. Step 5

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 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

Symmetry in an equilateral triangle

MATHVOX

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