Isosceles Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

isosceles triangle 1

  • A two-dimensional figure that 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.
  • Radius of a circumcircle (outer) of a isosceles triangle if given legs and hypotrnuse ( R ).
  • Radius of a inscribed circle (inner) of a isosceles triangle if given legs and hypotrnuse ( r ).
  • Semiperimeter of a right triangle is one half of the perimeter.
  • The total of angles equal \(\;x+y+z=180° \).
  • Edges \(\;A = C\;\)
  • Angles \(\;x = y\;\)
  • 3 edges
  • 3 vertexs
  • Sidess:  \(a\),  \(b\),  \(c\)
  • Angles:  \(A\),  \(B\),  \(C\)
  • Area:  \(K\)
  • Perimeter:  \(P\)
  • 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
  • Semi-perimeter:  \(s\)  -  One half of the perimeter
  • Inradius of triangle:  \(r\)
  • Outradius (circumcircle) of triangle:  \(R\)

isosceles triangle 1Area of an Isosceles Triangle formula

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

Where:

\(\large{ A }\) = 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

 

 

isosceles triangle 1Height of an Isosceles Triangle formula

\(\large{ h = 2 \frac {A}{b} }\)

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

Where:

\(\large{ h }\) = height

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

\(\large{ A }\) = 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

isosceles triangle 1Perimeter of an Isosceles Triangle formula

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

Where:

\(\large{ P }\) = perimeter

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

 

 

isosceles triangle 1Semiperimeter of an Isosceles Triangle formula

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

Where:

\(\large{ s }\) = semiperimeter

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

 

 

isosceles triangle 1Side of an Isosceles Triangle formula

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

\(\large{ b = P - 2\;a   }\)

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

Where:

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

\(\large{ h }\) = height

\(\large{ P }\) = perimeter

\(\large{ A }\) = area

 

Tags: Equations for Triangle