# Formulas and Tables

Elementary Geometry# Parallelogram

Diagonals of a parallelogram: \({d_1},\) \({d_2}\)

Consecutive angles: \(\alpha\), \(\beta\)

Angle between the diagonals: \(\varphi\)

Perimeter: \(P\)

Area: \(S\)

Altitude: \(h\)

- A parallelogram is a quadrilateral with two pairs of parallel sides.

- In a paralellogram, the opposite sides are equal and the opposite angles are equal.
- The sum of the consecutive angles of a parallelogram is equal to \(180^\circ:\)

\(\alpha + \beta = 180^\circ\) - A parallelogram in which all four angles are right angles is called a rectangle. A parallelogram in which all four sides are equal is called a rhombus.
- Relation between the sides and the diagonals of a parallelogram

\(d_1^2 + d_2^2 =\) \( 2\left( {{a^2} + {b^2}} \right)\) - Altitude of a parallelogram

\(h = b\sin \alpha =\) \( b\sin \beta\) - Perimeter of a parallelogram

\(P = 2\left({a + b} \right)\) - Area of a parallelogram

\(S = ah =\) \(ab\sin \alpha =\) \({\large\frac{1}{2}\normalsize} {d_1}{d_2}\sin \varphi \)