# 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 formulas

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

### 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 formulas

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

### Where:

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

$$\large{ P }$$ = perimeter

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