Geometry

Angles:

Triangles:

Sine cosine rule:

Vectors:

Triangle Formulas

$a^2 = b^2 + c^2 - 2bc \textrm{ cos } \alpha$
$b^2 = a^2 + c^2 - 2ac \textrm{ cos } \beta$
$a^2 = a^2 + b^2 - 2ab \textrm{ cos } \gamma$
$\frac{a}{\textrm{ sin } \alpha} = \frac{b}{\textrm{ sin } \beta} = \frac{c}{\textrm{ sin } \gamma} = 2R$

Median formulas:
$m_a^2 = \frac{1}{4}( 2b^2 + 2c^2 - a^2 )$
$m_b^2 = \frac{1}{4}( 2a^2 + 2c^2 - b^2 )$
$m_c^2 = \frac{1}{4}( 2a^2 + 2b^2 - c^2 )$

Bisector formulas:
$\frac{a}{b} = \frac{n}{m}$
$l_c^2 = ab - nm$

Right triangle formulas:
$c^2 = a^2 + b^2$
$A = \frac{1}{2}ab = \frac{1}{2}ch_c$
$a^2 = a_1c$
$b^2 = b_1c$
$h_c^2 = a_1.b_1$
$r = \frac{a + b - c}{2}$
${ sin }\alpha = \frac{a}{c}$
$\textrm{ cos }\alpha = \frac{b}{c}$
$\textrm{ tg }\alpha = \frac{a}{b}$
$\textrm{ cotg }\alpha = \frac{b}{a}$

Area Formulas

Area of a triagle: $A = \frac{1}{2}ch_c$
$A = \frac{1}{2}ab \textrm{ sin } \gamma$
$A = \sqrt{p(p - a)(p - b)(p - c)}$
$A = pr$
$A = \frac{abc}{4R}$
Area of a parallelogram: $A = ah_a$     $A = ab \textrm{ sin } \alpha$
Area of a rectangle: $A = \frac{1}{2}d_1d_2 \textrm{ sin } \phi$
Area of a prescribed polygon: $A = pr$

Geometry Practices:



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