Right Isosceles Triangle

Right isosceles triangle (a two-dimensional figure) has one side a right 90° interior angle and the other two angles are 45°.
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.
Hypotenuse of a right isosceles triangle is the longest side or the side opposite the right angle.
Inscribed circle is the Iargest circle possible that can fit on the inside of a two-dimensional figure.
Median of a right isosceles triangle is a line segment from a vertex (coiner point) to the midpoint of the opposite side.
Semiperimeter is one half of the perimeter.
Side of a right triangle is one half of the perimeter.
Two sides are congruent.
3 edges
3 vertexs
a = opposite leg
b = adjacent leg
c = hypotenuse
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

Angle bisector of a Right Isosceles Triangle formulas
\( t_a \;=\; 2 \cdot b \cdot c \cdot cos\left( \dfrac{ \dfrac{A}{2} }{ b + c } \right) \) \( t_a \;=\; \sqrt{ b \cdot c \cdot \dfrac{ 1 - a^2 }{ \left( b + c \right)^2 } } \) \( t_b \;=\; 2 \cdot a \cdot c \cdot cos\left( \dfrac{ \dfrac{B}{2} }{ a + c } \right) \) \( t_b \;=\; \sqrt{ a \cdot c \cdot \dfrac{ 1 - b^2 }{ \left( a + c \right)^2 } } \) \( t_c \;=\; a \cdot b \cdot \sqrt{ \dfrac{ 2 }{ a + b } } \)
Symbol	English	Metric
\( t_a, t_b, t_c \) = angle bisector	\( in \)	\( mm \)
\( A, B, C \) = angle	\( deg \)	\( rad \)
\( a, b, c \) = edge	\( in \)	\( mm \)

Area of a Right Isosceles Triangle formulas
\( A_{area} \;=\; \dfrac{ h \cdot b }{2} \) \( A_{area} \;=\; \dfrac{1}{2} \cdot b \cdot h \) \( A_{area} \;=\; a \cdot b \cdot \dfrac{ sin( y) }{ 2 } \)
Symbol	English	Metric
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( a, b, c \) = edge	\( in \)	\( mm \)
\( h \) = height	\( in \)	\( mm \)

Circumcircle of a Right Iosceles Triangle formulas
\( R \;=\; \dfrac{ 1 }{ 2 } \cdot \sqrt{ a^2 + b^2 } \) \( R \;=\; \dfrac{ H }{ 2 } \)
Symbol	English	Metric
\( R \) = outcircle	\( in \)	\( mm \)
\( a, b, c \) = edge	\( in \)	\( mm \)
\( H \) = hypotenuse	\( in \)	\( mm \)

Height of a Right Isosceles Triangle formula
\( h_c \;=\; 2 \cdot \dfrac{ A_{area} }{ b } \)
Symbol	English	Metric
\( h^c \) = height	\( in \)	\( mm \)
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( a, b, c \) = edge	\( in \)	\( mm \)

Inscribed Circle of a Right Isosceles Triangle formula
\( r \;=\; \dfrac{ a + b - c }{ 2 } \)
Symbol	English	Metric
\( r \) = incircle	\( in \)	\( mm \)
\( a, b, c \) = edge	\( in \)	\( mm \)

Median of a Right Isosceles Triangle formulas
\( m_a \;=\; \sqrt{ \dfrac{ 4 \cdot b^2 + a^2 }{ 2 } } \) \( m_b \;=\; \sqrt{ \dfrac{ 4 \cdot a^2 + b^2 }{ 2 } } \) \( m_c \;=\; \dfrac{c }{ 2} \)
Symbol	English	Metric
\( m_a, m_b, m_c \) = median	\( in \)	\( mm \)
\( a, b, c \) = edge	\( in \)	\( mm \)

Perimeter of a Right Isosceles Triangle formula
\( P \;=\; a + b + c \)
Symbol	English	Metric
\( P \) = perimeter	\( in \)	\( mm \)
\( a, b, c \) = edge	\( in \)	\( mm \)

Side of a Right Isosceles Triangle formula
\( a \;=\; P - b - c \) \( a \;=\; 2\cdot \dfrac{A_{area} }{ b \cdot sin( y) } \) \( b \;=\; P - a - c \) \( b \;=\; 2 \cdot \dfrac{A_{area} }{ h} \) \( c \;=\; P - a - b \)
Symbol	English	Metric
\( a, b, c \) = edge	\( in \)	\( mm \)
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( P \) = 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 : \(\; Area \;=\;\dfrac{ a \cdot b }{ 2 }\)