# Parallelogram

• Sides of a parallelogram: $$a$$, $$b$$
Diagonals of a parallelogram: $${d_1},$$ $${d_2}$$
Consecutive angles: $$\alpha$$, $$\beta$$
Angle between the diagonals: $$\varphi$$
Perimeter: $$P$$
Area: $$S$$
Altitude: $$h$$
1. A parallelogram is a quadrilateral with two pairs of parallel sides.
2. In a paralellogram, the opposite sides are equal and the opposite angles are equal.
3. The sum of the consecutive angles of a parallelogram is equal to $$180^\circ:$$
$$\alpha + \beta = 180^\circ$$
4. 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.
5. Relationship between the sides and the diagonals of a parallelogram
$$d_1^2 + d_2^2 =$$ $$2\left( {{a^2} + {b^2}} \right)$$
6. Altitude of a parallelogram
$$h = b\sin \alpha =$$ $$b\sin \beta$$
7. Perimeter of a parallelogram
$$P = 2\left({a + b} \right)$$
8. Area of a parallelogram
$$S = ah =$$ $$ab\sin \alpha =$$ $${\large\frac{1}{2}\normalsize} {d_1}{d_2}\sin \varphi$$