Isosceles Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Isosceles Triangleisosceles triangle 2isosceles triangle 1

  • An isosceles triangle is when two sides are equal and two angles are equal.
  • 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 (coiner 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:  \(R\)

 

Area of an Isosceles Triangle

Area of an Isosceles Triangle formula

\(A= \frac {hb} {2} \)

Where:

\(A\) = area

\(b\) = side

\(h\) = height

Circumcircle of an Isosceles Triangle

The radius of a circumcircle (outer) of a an Isosceles triangle if given side \(( R )\).

Circumcircle of an Isosceles Triangle formula

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

Where:

\(R\) = outcircle

\(a, b\) = side

Height of an Isosceles Triangle

Height of an Isosceles Triangle formula

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

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

Where:

\(h\) = height

\(a, b\) = side

\(A\) = area

Inscribed Circle of an Isosceles Triangle

Inscribed Circle of an Isosceles Triangle formula

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

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

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

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

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

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

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

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

Where:

\(r\) = incircle

\(a, b\) = side

\(\alpha\) (Greek symbol alpha) = angle

\(h\) = height

Perimeter of an Isosceles Triangle

Perimeter of an Isosceles Triangle formula

\(P = 2a + b \)

Where:

\(P\) = perimeter

\(a, b\) = side

Semiperimeter of an Isosceles Triangle

One half of the perimeter.

Semiperimeter of an Isosceles Triangle formula

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

Where:

\(s\) = semiperimeter

\(a, b, c\) = side

Side of an Isosceles Triangle

Side of an Isosceles Triangle formula

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

\(b = P - 2a   \)

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

Where:

\(a, b\) = side

\(h\) = height

\(P\) = perimeter

\(A\) = area

 

Tags: Equations for Triangle