Isosceles Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

isosceles triangle 1

  • Isosceles triangle (a two-dimensional figure) has two sides that are the same length or at least two congruent sides.
  • Angle bisector of a right isosceles 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.
  • Congruent is all sides having the same lengths and angles measure the same.
  • Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
  • Semiperimeter is one half of the perimeter.
  • a = c
  • x = y
  • x + y + z = 180°
  • 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
  • 3 edges
  • 3 vertexs

Area of an Isosceles Triangle formula

\(\large{ A_{area} = \frac {h\;b} {2} }\)

Where:

\(\large{ A_{area} }\) = area

\(\large{ b }\) = side

\(\large{ h }\) = height

isosceles triangle 2Circumcircle of an Isosceles Triangle formula

\(\large{ R =  \frac  { a^2 } { \sqrt {  4\; a^2 \;-\; b^2   } }  }\)

Where:

\(\large{ R }\) = outcircle

\(\large{ a, b }\) = side

 

 

Height of an Isosceles Triangle formula

\(\large{ h = 2 \frac {A_{area}}{b} }\)

\(\large{ h = \sqrt {   a^2 - \frac {b^2}{4}  } }\)

Where:

\(\large{ h }\) = height

\(\large{ a, b }\) = side

\(\large{ A_{area} }\) = area

isosceles triangle 2Inscribed Circle of an Isosceles Triangle formula

The radius of a inscribed circle (inner) of an Isosceles triangle if given side \(( r )\).

\(\large{ r =   \frac { b } { 2 } \; \sqrt  {   \frac  { 2\;a \;-\; b  }  {  2\;a \;+\; b }   } }\)

The radius of a inscribed circle (inner) of an Isosceles triangle if given side and angle \(( r )\).

\(\large{ r =   a \;  \frac { sine \; \alpha \;x\; cos \; \alpha } { 1  \;+\;  cos \; \alpha }  =  \alpha \; cos \; \alpha \;\;x\;\;  tan \frac  { \alpha }  {  2 }  }\)

\(\large{ r =  \frac {b}{2}  \;x\;   \frac { sine \; \alpha } { 1  \;+\;  cos \; \alpha }  =   \frac {b}{2}  \;x\;  tan \frac  { \alpha }  {  2 }  }\)

The radius of a inscribed circle (inner) of an Isosceles triangle if given side and height \(( r ) \).

\(\large{ r =   \frac { b\;h } {  b \;+\;  \sqrt  { 4\;h^2 \;+\; b^2  }   } }\)

\(\large{ r =   \frac {  h\;  \sqrt  { a^2 \;-\; h^2  }  } {  a \;+\;  \sqrt  { a^2 \;-\; h^2  }   } }\)

Where:

\(\large{ r }\) = incircle

\(\large{ a, b }\) = side

\(\large{ \alpha }\)  (Greek symbol alpha) = angle

\(\large{ h }\) = height

Perimeter of an Isosceles Triangle formula

\(\large{ P = 2\;a + b }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ a, b }\) = side

Semiperimeter of an Isosceles Triangle formula

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

Where:

\(\large{ s }\) = semiperimeter

\(\large{ a, b, c }\) = side

Side of an Isosceles Triangle formula

\(\large{ a = \frac {P} {2} - \frac {b} {2} }\)

\(\large{ b = P - 2\;a   }\)

\(\large{ b = 2\; \frac {A_{area}} {h} }\)

Where:

\(\large{ a, b }\) = side

\(\large{ h }\) = height

\(\large{ P }\) = perimeter

\(\large{ A_{area} }\) = area

 

Tags: Equations for Triangle