# Equilateral Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

## • Equilateral triangle (a two-dimensional figure) has three sides that are the same length and all sides and angles are congruent.
• A equilateral triangle is a polygon.
• Angle bisector of a equilateral triangle is a line that splits an angle into two equal angles.
• Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
• Height of a equilateral triangle is the length of the two sides and the perpendicular height of the 90 degree angle.
• Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
• Median of a equilateral triangle is a line segment from a vertex (coiner point) to the midpoint of the opposite side.
• Semiperimeter is one half of the perimeter.
• x + y + z = 180°
• 3 edges
• 3 vertexs
• Sides:  a, b, c
• Angles:  ∠A, ∠B, ∠C
• Height:  $$h_a$$, $$h_b$$, $$h_c$$
• Median:  $$m_a$$, $$m_b$$, $$m_c$$  -  A line segment from a vertex (corner point) to the midpoint of the opposite side
• Angle bisectors:  $$t_a$$, $$t_b$$, $$t_c$$  -  A line that splits an angle into two equal angles

### Angle bisector of an Equilateral Triangle formula

$$\large{ t_a, t_b, t_c = a \; \sqrt{ \frac{ 3 }{ 2 } } }$$

Where:

$$\large{ t_a, t_b, t_c }$$ = angle bisector

$$\large{ a, b, c }$$ = edge

### Area of an Equilateral Triangle formula

$$\large{ A_{area} = \frac{ \sqrt{3} }{4}\; a^2 }$$

Where:

$$\large{ A_{area} }$$ = area

$$\large{ a, b, c }$$ = edge

### Circumcircle of an Equilateral Triangle formula

$$\large{ R = \frac{ a }{ \sqrt {3 } } }$$

$$\large{ R = \frac{ 2\;h }{ 3 } }$$

Where:

$$\large{ R }$$ = outcircle

$$\large{ a, b, c }$$ = edge

$$\large{ h }$$ = height

### Height of an Equilateral Triangle formula

$$\large{ h_a, h_b, h_c = a \sqrt { \frac{ 3 }{ 2 } } }$$

Where:

$$\large{ h_a, h_b, h_c }$$ = height

$$\large{ a, b, c }$$ = edge

### Inscribed Circle of an Equilateral Triangle formula

$$\large{ r = \frac{ a }{ 2\; \sqrt{ 3 } } }$$

Where:

$$\large{ r }$$ = incircle

$$\large{ a, b, c }$$ = edge

### Median of an Equilateral Triangle formula

$$\large{ m_a, m_b, m_c = a \; \sqrt { \frac{ 3 }{ 2 } } }$$

Where:

$$\large{ m_a, m_b, m_c }$$ = median

$$\large{ a, b, c }$$ = edge

### Perimeter of an Equilateral Triangle formula

$$\large{ P = 3\;a }$$

Where:

$$\large{ P }$$ = perimeter

$$\large{ a, b, c }$$ = edge

### Semiperimeter of an Equilateral Triangle formula

$$\large{ s = \frac{ a + b + c }{ 2 } }$$

Where:

$$\large{ s }$$ = semiperimeter

$$\large{ a, b, c }$$ = edge

### Side of an Equilateral Triangle formula

$$\large{ a = \frac {P}{3} }$$

$$\large{ a = \frac{2}{3}\; 3^{3/4} \sqrt{A_{area}} }$$

Where:

$$\large{ a, b, c }$$ = edge

$$\large{ P }$$ = perimeter

$$\large{ A_{area} }$$ = area