# Right Isosceles Triangle

7.1 #13 Finding the lengths of two legs of an isosceles right triangle when given the hypotenuse
7.1 #13 Finding the lengths of two legs of an isosceles right triangle when given the hypotenuse

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
• 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 $$\large{ t_a = 2\;b\;c \;\; cos \; \frac { \frac {A}{2} }{ b \;+\; c } }$$ $$\large{ t_a = \sqrt { bc \; \frac { 1 \;-\; a^2 } { \left( b \;+\; c \right)^2 } } }$$ $$\large{ t_b = 2\;a\;c \;\; cos \; \frac { \frac {B}{2} }{ a \;+\; c } }$$ $$\large{ t_b = \sqrt { a\;c \; \frac { 1 \;-\; b^2 } { \left( a \;+\; c \right)^2 } } }$$ $$\large{ t_c = a\;b \; \sqrt { \frac { 2 }{ a \;+\; b } } }$$ Symbol English Metric $$\large{ t_a, t_b, t_c }$$ = angle bisector $$\large{ in }$$ $$\large{ mm }$$ $$\large{ A, B, C }$$ = angle $$\large{ deg }$$ $$\large{ rad }$$ $$\large{ a, b, c }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
 Area of a Right Isosceles Triangle formulas $$\large{ A_{area} = \frac {h\;b} {2} }$$ $$\large{ A_{area} = \frac {1} {2}\; b\;h }$$ $$\large{ A_{area} = a\;b\; \frac {\sin \;y} {2} }$$ Symbol English Metric $$\large{ A_{area} }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$ $$\large{ a, b, c }$$ = edge $$\large{ in }$$ $$\large{ mm }$$ $$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
 Circumcircle of a Right sosceles Triangle formulas $$\large{ R = \frac { 1 } { 2 } \; \sqrt { a^2 + b^2 } }$$ $$\large{ R = \frac { H } { 2 } }$$ Symbol English Metric $$\large{ R }$$ = outcircle $$\large{ in }$$ $$\large{ mm }$$ $$\large{ a, b, c }$$ = edge $$\large{ in }$$ $$\large{ mm }$$ $$\large{ H }$$ = hypotenuse $$\large{ in }$$ $$\large{ mm }$$
 Height of a Right Isosceles Triangle formula $$\large{ h_c = 2\; \frac {A_{area}}{b} }$$ Symbol English Metric $$\large{ h^c }$$ = height $$\large{ in }$$ $$\large{ mm }$$ $$\large{ A_{area} }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$ $$\large{ a, b, c }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
 Inscribed Circle of a Right Isosceles Triangle formula $$\large{ r = \frac { a \;+\; b \;-\; c } { 2 } }$$ Symbol English Metric $$\large{ r }$$ = incircle $$\large{ in }$$ $$\large{ mm }$$ $$\large{ a, b, c }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
 Median of a Right Isosceles Triangle formulas $$\large{ m_a = \sqrt { \frac { 4\;b^2 \;+\; a^2 }{ 2 } } }$$ $$\large{ m_b = \sqrt { \frac { 4\;a^2 \;+\; b^2 }{ 2 } } }$$ $$\large{ m_c = \frac {c} {2} }$$ Symbol English Metric $$\large{ m_a, m_b, m_c }$$ = median $$\large{ in }$$ $$\large{ mm }$$ $$\large{ a, b, c }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
 Perimeter of a Right Isosceles Triangle formula $$\large{ P = a + b + c }$$ Symbol English Metric $$\large{ P }$$ = perimeter $$\large{ in }$$ $$\large{ mm }$$ $$\large{ a, b, c }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
 Side of a Right Isosceles Triangle formula $$\large{ a = P – b – c }$$ $$\large{ a = 2\; \frac {A_{area}} {b\;\sin y} }$$ $$\large{ b = P – a – c }$$ $$\large{ b = 2\; \frac {A_{area}}{h} }$$ $$\large{ c = P – a – b }$$ Symbol English Metric $$\large{ a, b, c }$$ = edge $$\large{ in }$$ $$\large{ mm }$$ $$\large{ A_{area} }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$ $$\large{ P }$$ = perimeter $$\large{ in }$$ $$\large{ mm }$$
 Trig Functions Find A Find B Find a Find b Find c Find Area

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