Pythagorean Theorem and Special Right Triangles

Pythagorean theorem

Right triangle

a^{2} + b^{2} = c^{2}

c the hypotenuse

Acute triangle

c^{2} < a^{2} + b^{2}

c the longest side

Obtuse triangle

c^{2} > a^{2} + b^{2}

c the longest side

45°-45°-90°

x : x : x \sqrt{2}

30°-60°-90°

x : x \sqrt{3} : 2 x

Altitude

h^{2} = p q

p and q the two parts of the hypotenuse

Legs

a^{2} = p c b^{2} = q c

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