Isosceles Triangle

Isosceles triangle (a two-dimensional figure) has two sides that are the same length or at least two congruent sides.
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
\( A_{area} \;=\; \dfrac{ h \cdot b }{ 2 } \)
Symbol	English	Metric
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( a, b, c \) = side	\( in \)	\( mm \)
\( h \) = height	\( in \)	\( mm \)

Circumcircle of an Isosceles Triangle formula
\( R \;=\; \dfrac{ a^2 }{ \sqrt{ 4 \cdot a^2 - b^2 } } \)
Symbol	English	Metric
\( R \) = outcircle	\( in^2 \)	\( mm^2 \)
\( a, b, c \) = side	\( in \)	\( mm \)
\( h \) = height	\( in \)	\( mm \)

Height of an Isosceles Triangle formula
\( h \;=\; 2 \cdot \dfrac {A_{area} }{ b } \) \( h \;=\; \sqrt{ a^2 - \dfrac{ b^2 }{ 4 } } \)
Symbol	English	Metric
\( h \) = height	\( in \)	\( mm \)
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( a, b, c \) = side	\( in \)	\( mm \)

Inscribed Circle of an Isosceles Triangle formulas The radius of a inscribed circle (inner) of an Isosceles triangle if given side \(( r )\)
\( r \;=\; \dfrac{ b }{ 2 } \cdot \sqrt{ \dfrac{ 2 \cdot a - b }{ 2 \cdot a + b } } \) \( r \;=\; a \cdot \dfrac{ sine( \alpha) \cdot cos( \alpha) }{ 1 + cos( \alpha) } \;=\; \alpha \cdot cos( \alpha) \cdot tan\left( \dfrac{ \alpha }{ 2 } \right) \) \( r \;=\; \dfrac{ b}{2} \cdot \dfrac{ sine( \alpha) }{ 1 + cos( \alpha) } \;=\; \dfrac {b}{2} \cdot tan\left( \dfrac{ \alpha }{ 2 } \right) \) \( r \;=\; \dfrac{ b \cdot h }{ b + \sqrt{ 4 \cdot h^2 + b^2 } } \) \( r \;=\; \dfrac{ h \cdot \sqrt{ a^2 - h^2 } }{ a + \sqrt{ a^2 - h^2 } } \)
Symbol	English	Metric
\( r \) = incircle	\( in \)	\( mm \)
\( \alpha \) (Greek symbol alpha) = angle	\( deg \)	\( rad \)
\( a, b, c \) = side	\( in \)	\( mm \)
\( h \) = height	\( in \)	\( mm \)

Perimeter of an Isosceles Triangle formula
\( P \;=\; 2 \cdot a + b \)
Symbol	English	Metric
\( P \) = perimeter	\( in \)	\( mm \)
\( a, b, c \) = side	\( in \)	\( mm \)

Semiperimeter of an Isosceles Triangle formula
\( s \;=\; \dfrac{ a + b + c }{ 2 } \)
Symbol	English	Metric
\( s \) = semiperimeter	\( in \)	\( mm \)
\( a, b, c \) = side	\( in \)	\( mm \)

Side of an Isosceles Triangle formulas
\( a \;=\; \dfrac{P}{2} - \dfrac{b}{2} \) \( b \;=\; P - 2 \cdot a \) \( b \;=\; 2 \cdot \dfrac{A_{area} }{ h } \)
Symbol	English	Metric
\( a, b, c \) = side	\( in \)	\( mm \)
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( h \) = height	\( in \)	\( mm \)
\( P \) = perimeter	\( in \)	\( mm \)

Trig Functions
Find A given a c : \(\; sin( A) \;=\; \dfrac{ a }{ c }\) given b c : \(\; cos( A) \;=\; \dfrac{ b }{ c }\) given a b : \(\; tan( A) \;=\; \dfrac{ a }{ b }\)
Find B given a c : \(\; sin( B) \;=\; \dfrac{ a }{ c }\) given b c : \(\; cos( B) \;=\; \dfrac{ b }{ c }\) given a b : \(\; tan( B) \;=\; \dfrac{ b }{ a }\)
Find a given A c : \(\; a \;=\; c \cdot sin( A) \) given A b : \(\; a \;=\; b \cdot tan( A) \)
Find b given A c : \(\; b \;=\; c \cdot cos( A) \) given A a : \(\; b \;=\; \dfrac{ a }{ tan( A) }\)
Find c given A a : \(\; c \;=\; \dfrac{ a }{ sin( A) }\) given A b : \(\; c \;=\; \dfrac{ b }{ cos( A) }\) given a b : \(\; c \;=\; \sqrt{ a^2 + b^2 } \)
Find Area given a b : \(\; Area \;=\; \dfrac{ a \cdot b }{ 2 }\)