- The parallelogram is a convex figure.
- The sum of the measures of all interior angles is 2Π (360°), and the sum of the measures of two adjacent interior angles is Π, $$ \alpha + \beta = 180° $$

is: $$ \alpha = 180° – \beta $$ $$ \beta = 180° – \alpha $$
- The sum of the measures of two adjacent angles at which the diagonals intersect is Π, $$ \gamma + \delta = 180° $$

as a result of: $$ \gamma = 180° – \delta $$ $$ \delta = 180° – \gamma $$
- The point of intersection of the diagonals of the parallelogram divides each of them into halves.
- Formula on the longer diagonal of the parallelogram from the sides and the angle α
$$ f= \sqrt{a^2+2ab \cos \alpha\ +b^2} $$

- Formula on the longer diagonal of the parallelogram from the sides and the angle β
$$ f= \sqrt{a^2-2ab \cos \beta\ +b^2} $$

- Formula on the longer diagonal of the parallelogram from the sides and the shorter diagonal
$$ f= \sqrt{2a^2 + 2b^2 – e^2} $$

- Formula for the longest diagonal of the parallelogram from the field, the shorter diagonal and the angle between the diagonals
$$ f= \frac{2S}{e\cdot \sin \gamma} = \frac{2S}{e\cdot \sin \delta} $$

- Formula for the shorter diagonal of the parallelogram from the sides and the angle α
$$ e= \sqrt{a^2-2ab \cos \alpha\ +b^2} $$

- Formula for the shorter diagonal of the parallelogram from the sides and the angle β
$$ e= \sqrt{a^2+2ab \cos \beta\ +b^2} $$

- Formula for the shorter diagonal of the parallelogram from the sides and the longer diagonal
$$ e= \sqrt{2a^2 + 2b^2 – f^2} $$

- Formula for the shorter diagonal of the parallelogram from the field, the longer diagonal and the angle between the diagonals
$$ e= \frac{2S}{f\cdot \sin \gamma} = \frac{2S}{f\cdot \sin \delta} $$

- Formula for the height of the parallelogram from the side and the area
$$ h_1=\frac{S}{a}; h_2=\frac{S}{b} $$

- Formula for the height of the parallelogram from the side and angle
$$ h_1=b \cdot \sin \alpha; h_2=a \cdot \sin \alpha$$

- Formula for the height of a parallelogram from perimeter, side, and angle
$$ h_1=\frac{(L-2a) \cdot \sin \alpha}{2}; h_2=\frac{(L-2b) \cdot \sin \alpha}{2} $$

- Formula for the area of the parallelogram from the side and height
$$ S=a\cdot h_1; S=b\cdot h_2 $$

- Formula for the area of the parallelogram from the sides and angle(α) or (β)
$$ S=a\cdot b \cdot \sin \alpha; S=a\cdot b \cdot \sin \beta $$

- Formula for the area of a parallelogram from diagonals and angle(γ) or (δ)
$$ S=\frac {e \cdot f \cdot \sin \gamma}{2}; S=\frac {e \cdot f \cdot \sin \delta}{2} $$

- Formula for the perimeter of the parallelogram from the sides
$$ L = 2a+2b = 2(a+b) $$

- Formula for the perimeter of the parallelogram from the side and diagonals
$$ L = 2a+\sqrt{2e^2+2f^2-4a^2};$$ $$ L = 2b+\sqrt{2e^2+2f^2-4b^2} $$

- Formula for the perimeter of the parallelogram from the side, height and angle α
$$ L = 2(a + \frac {h_1}{\sin \alpha});$$ $$ L = 2(b + \frac {h_2}{\sin \alpha}) $$

- Formula for the sides of the parallelogram from diagonals and angle of intersection of diagonals
$$ a=\frac {\sqrt{e^2+f^2+2ef\cdot\cos \gamma}}{2}; a=\frac {\sqrt{e^2+f^2-2ef\cdot\cos \delta}}{2} $$

$$ b=\frac {\sqrt{e^2+f^2-2ef\cdot\cos \gamma}}{2}; b=\frac {\sqrt{e^2+f^2+2ef\cdot\cos \delta}}{2} $$

- Formula for the side of the parallelogram from the other side and diagonals
$$ a=\frac {\sqrt {2e^{2}+2f^{2}-4b^2}}{2} $$ $$ b=\frac {\sqrt {2e^{2}+2f^{2}-4a^2}}{2} $$

- Formula for the sides of the parallelogram from height and angle α

$$ a=\frac {h_2}{\sin \alpha} $$ $$ b=\frac {h_1}{\sin \alpha} $$