Equilateral Triangle

on 29 January 2016. 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

equilateral triangle 4

angle bisector of an Equilateral triangle formula
\(\large{ t_a,\; t_b, \;t_c = a \; \sqrt{ \frac{ 3 }{ 2 } } }\)
Symbol	English	Metric
\(\large{ t_a, t_b, t_c }\) = angle bisector	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ a, b, c }\) = edge	\(\large{ in }\)	\(\large{ mm }\)

area of an Equilateral triangle formula
\(\large{ A_{area} = \frac{ \sqrt{3} }{4}\; a^2 }\)
Symbol	English	Metric
\(\large{ A_{area} }\) = area	\(\large{ in^2 }\)	\(\large{ mm^2 }\)
\(\large{ a, b, c }\) = edge	\(\large{ in }\)	\(\large{ mm }\)

circumcircle of an Equilateral triangle formulas
\(\large{ R = \frac{ a }{ \sqrt {3 } } }\) \(\large{ R = \frac{ 2\;h }{ 3 } }\)
Symbol	English	Metric
\(\large{ R }\) = outcircle	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ a, b, c }\) = edge	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ h }\) = height	\(\large{ in }\)	\(\large{ mm }\)

equilateral triangle 4

height of an Equilateral triangle formula
\(\large{ h_a, \;h_b, \;h_c = a \; \sqrt { \frac{ 3 }{ 2 } } }\)
Symbol	English	Metric
\(\large{ h_a, h_b, h_c }\) = height	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ a, b, c }\) = edge	\(\large{ in }\)	\(\large{ mm }\)

inscribed circle of an Equilateral triangle formula
\(\large{ r = \frac{ a }{ 2\; \sqrt{ 3 } } }\)
Symbol	English	Metric
\(\large{ r }\) = incircle	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ a, b, c }\) = edge	\(\large{ in }\)	\(\large{ mm }\)

median of an Equilateral triangle formula
\(\large{ m_a, \;m_b, \;m_c = a \; \sqrt { \frac{ 3 }{ 2 } } }\)
Symbol	English	Metric
\(\large{ m_a, m_b, m_c }\) = median	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ a, b, c }\) = edge	\(\large{ in }\)	\(\large{ mm }\)

perimeter of an Equilateral triangle formula
\(\large{ P = 3\;a }\)
Symbol	English	Metric
\(\large{ P }\) = perimeter	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ a, b, c }\) = edge	\(\large{ in }\)	\(\large{ mm }\)

semiperimeter of an Equilateral triangle formula
\(\large{ s = \frac{ a \;+\; b \;+\; c }{ 2 } }\)
Symbol	English	Metric
\(\large{ s }\) = semiperimeter	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ a, b, c }\) = edge	\(\large{ in }\)	\(\large{ mm }\)

side of an Equilateral triangle formulas
\(\large{ a = \frac {P}{3} }\) \(\large{ a = \frac{2}{3}\; 3^{3/4}\; \sqrt{A_{area}} }\)
Symbol	English	Metric
\(\large{ a, b, c }\) = edge	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ A_{area} }\) = area	\(\large{ in^2 }\)	\(\large{ ^2 }\)
\(\large{ P }\) = perimeter	\(\large{ in }\)	\(\large{ mm }\)

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angle bisector of an Equilateral triangle formula