Equilateral Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

equilateral triangle 1

  • 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

 

equilateral triangle 4Formulas that use Equilateral triangle Angle bisector

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

Where:

\(\large{ t_a,\; t_b,\; t_c }\) = angle bisector

\(\large{ a,\; b, \;c }\) = edge

 

 

Formulas that use Equilateral triangle area

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

Where:

\(\large{ A_{area} }\) = area

\(\large{ a, \;b, \;c }\) = edge

 

equilateral triangle 3Formulas that use Equilateral triangle Circumcircle

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

Where:

\(\large{ R }\) = outcircle

\(\large{ a, \;b, \;c }\) = edge

\(\large{ h }\) = height

 

equilateral triangle 4Formulas that use Equilateral triangle Height

\(\large{ h_a, \;h_b, \;h_c = a \; \sqrt {  \frac{ 3 }{ 2 }   } }\)   

Where:

\(\large{ h_a, \;h_b, \;h_c }\) = height

\(\large{ a, \;b, \;c }\) = edge

 

 

 

equilateral triangle 3Formulas that use Equilateral triangle Inscribed Circle

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

Where:

\(\large{ r }\) = incircle

\(\large{ a, \;b,\; c }\) = edge

 

 

equilateral triangle 4Formulas that use Equilateral triangle Median

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

Where:

\(\large{ m_a,\; m_b, \;m_c }\) = median

\(\large{ a,\; b,\; c }\) = edge

 

 

 

Formulas that use Equilateral triangle Perimeter

\(\large{ P = 3\;a }\)   

Where:

\(\large{ P }\) = perimeter

\(\large{ a,\; b, \;c }\) = edge

 

Formulas that use Equilateral triangle Semiperimeter

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

Where:

\(\large{ s }\) = semiperimeter

\(\large{ a,\; b, \;c }\) = edge

 

Formulas that use Equilateral triangle Side

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

Where:

\(\large{ a, \;b, \;c }\) = edge

\(\large{ P }\) = perimeter

\(\large{ A_{area} }\) = area

 

Tags: Equations for Triangle