Formulas & tables/Mathematics/Plane geometry

Plane geometry

12 formulas · Mathematics

Pythagorean theorem
a2+b2=c2a^2+b^2=c^2
Law of sines
asin⁡α=bsin⁡β=csin⁡γ=2R\dfrac{a}{\sin\alpha}=\dfrac{b}{\sin\beta}=\dfrac{c}{\sin\gamma}=2R
Law of cosines
c2=a2+b2−2abcos⁡γc^2=a^2+b^2-2ab\cos\gamma
Area of a triangle (base and height)
P=12ahP=\tfrac12 a h
Area of a triangle (two sides and the included angle)
P=12absin⁡γP=\tfrac12 ab\sin\gamma
Heron's formula
P=s(s−a)(s−b)(s−c)P=\sqrt{s(s-a)(s-b)(s-c)}
Area of an equilateral triangle
P=a234P=\dfrac{a^2\sqrt{3}}{4}
Area of a circle
P=πr2P=\pi r^2
Circumference of a circle
L=2πrL=2\pi r
Arc length
l=α360∘⋅2πrl=\dfrac{\alpha}{360^\circ}\cdot 2\pi r
Area of a circular sector
P=α360∘⋅πr2P=\dfrac{\alpha}{360^\circ}\cdot \pi r^2
Thales's theorem (intercept theorem)
∣AB∣∣BC∣=∣A′B′∣∣B′C′∣\dfrac{|AB|}{|BC|}=\dfrac{|A'B'|}{|B'C'|}