
Parallelogram. Formulas and Properties of a Parallelogram
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Definition of a parallelogram
Characterizations of a parallelogram
The basic properties of a parallelogram
The sides of a parallelogram
The diagonal of a parallelogram
The perimeter of a parallelogram
The area of a parallelogram
Definition. Parallelogram is a quadrilateral whose opposite sides are parallel and pairwise equal(lie on parallel lines)..Parallelograms differ in size of an adjacent sides and angles but opposite angles is equal.
Characterizations of a parallelogramQuadrilateral ABCD is a parallelogram, if at least one of the following conditions:
1. Quadrilateral has two pairs of parallel sides:
2. Quadrilateral has a pair of parallel sides with equal lengths:
3. Opposite sides are equal in the quadrilateral:
4. Opposite angles are equal in the quadrilateral:
5. Diagonals bisect the intersection point in the quadrilateral:
6. The sum of the quadrilateral angles adjacent to any side is 180°:
7. The sum of the diagonals squares equals the sum of the sides squares in the quadrilateral:
The basic properties of a parallelogramSquare, rectangle and rhombus is a parallelogram.
1. Opposite sides of a parallelogram have the same length:
2. Opposite sides of a parallelogram are parallel:
3. Opposite angles of a parallelogram are equal:
4. Sum of the parallelogram angles is equal to 360°:
5. The sum of the parallelogram angles adjacent to any sides is 180°:
6. Each diagonal divides the parallelogram into two equal triangle
7. Two diagonals is divided parallelogram into two pairs of equal triangles
8. The diagonals of a parallelogram intersect and intersection point separating each one in half:
9. Intersection point of the diagonals is called a center of parallelogram symmetry
10. Sum of the diagonals squares equals the sum of sides squares in parallelogram:
11. Bisectors of parallelogram opposite angles are always parallel
12. Bisectors of parallelogram adjacent angles always intersect at right angles (90°)
The sides of a parallelogramSides of a parallelogram formulas:1. Formula of parallelogram sides in terms of diagonal and angle between the diagonals:
2. Formula of parallelogram sides in terms of diagonals and other side:
3. Formula of parallelogram sides in terms of altitude (height) and sine of an angle:
4. Formula of parallelogram sides in terms of area and altitude (height):
The diagonal of a parallelogramDefinition. The diagonal of a parallelogram is any segment that connects two vertices of a parallelogram opposite angles.Parallelogram has two diagonally  a longer let be d_{1}, and shorter  d_{2}
Diagonal of a parallelogram formulas:1. Formula of parallelogram diagonal in terms of sides and cosine β (cosine theorem)
2. Formula of parallelogram diagonal in terms of sides and cosine α (cosine theorem)
3. Formula of parallelogram diagonal in terms of two sides and other diagonal:
4. Formula of parallelogram diagonal in terms of area, other diagonal and angles between diagonals:
The perimeter of a parallelogramDefinition. The perimeter of a parallelogram is the sum of the all parallelogram sides lengths.Perimeter of a parallelogram formulas:1. Formula of parallelogram perimeter in terms of sides:
2. Formula of parallelogram perimeter in terms of one side and diagonals:
3. Formula of parallelogram perimeter in terms of side, height and sine of an angle:
The area of a parallelogramDefinition. The area of a parallelogram the space is restricted parallelogram sides or within the perimeter of a parallelogram.Area of a parallelogram formulas:1. Formula of parallelogram area in terms of side and height:
A = b · h_{b} 2. Formula of parallelogram area in terms of sides and sine of an angle between this sides:
3. Formula of parallelogram area in terms of diagonals and sine of an angle between diagonals:
Geometry formulas
Square. Formulas and Properties of a Square
Rectangle. Formulas and Properties of a Rectangle
Parallelogram. Formulas and Properties of a Parallelogram
Rhombus. Formulas and Properties of a Rhombus
Area formulae of geometric shapes
Formulae perimeter of geometric shapes
Formulae for the volume of geometric shapes
Formulae surface area geometrical shapes Add the comment 