1.  Sides of a parallelogram if you know diagonals and angle between them or other side

- smaller  side

- larger  side

,       -  diagonals

,      -  angles between the diagonals

Find length of sides of a parallelogram if given diagonals and angle between the diagonals ( a b ) :

Find length of sides of a parallelogram if given diagonals and other side ( a b ) :

2.  Sides of a parallelogram if you know angle and height

,      -  angles

,      -  sides

- height  measured at right angles to the base

- height  measured at right angles to the base

Find sides of a parallelogram if given angle and height ( a b ) :

1.  Diagonals of a parallelogram if you know sides and angle or sides and other diagonal

- smaller  diagonal

- larger  diagonal

,       -  sides

-  acute angle

-  obtuse angle

Find length of diagonals of a parallelogram if given sides and angle ( D d /) :

Find length of diagonal of a parallelogram if given sides and other diagonal ( D d ) :

2.  Diagonals of a parallelogram if you know area, angle between the diagonals and other diagonal

- smaller  diagonal

- larger  diagonal

,      -  angles between the diagonals

- area  of a parallelogram

Find length of diagonal of a parallelogram if given area, angle between the diagonals and other diagonal ( D d ) :

- smaller  diagonal

- larger  diagonal

,      -  sides

-  acute angle

-  obtuse angle

-  area of a parallelogram

Find the angle of a parallelogram if given sides and diagonal  :

Find the angle of a parallelogram if given sides and area  :

Equations for the relation of the acute and obtuse angles:  :

- smaller  diagonal

- larger  diagonal

,      -  sides

-  acute angle  between diagonals

- obtuse angle  between diagonals

-  area of a parallelogram

Find the angle between diagonals if given sides and diagonals  :

Find the angle between diagonals if given area of a parallelogram and diagonals  :

Identities for the relation of the acute and obtuse angles between diagonals:  :

•  ,       -  sides

-  acute angle

-  obtuse angle

-  height to the base

-  height to the base

Find the length of the height of a parallelogram without area if given side and angle  :

The acute angle of intersection of the heights is equal to the acute angle of the parallelogram.  :
The obtuse angle of intersection of the heights is equal to the obtuse angle of a parallelogram.  :

- smaller  diagonal

- larger  diagonal

-  smaller side

-  larger side

-  acute angle between the diagonals

Equation for the sum of the squared diagonals  :

Equation for the difference of squares of the sides:  :

`1.  Properties of a bisector of a parallelogram  `
By definition, the bisector divides the angle in halves  :
The bisector cuts out an isosceles triangle (in this case, the triangles ABF and DKC)  :
The bisectors of the supplementary angles intersect at a right angle  :
The bisectors of the opposite angles are equal and parallel  :

-  bisector of an acute angle

-  bisector of an obtuse angle

,     -  sides of a parallelogram

-  acute angle

-  obtuse angle

Since ABF and DKC are isosceles triangles, the following identities hold  :

`2.  The length of a bisector of a parallelogram`

,       -  sides of a parallelogram

-  acute angle

-  obtuse angle

- bisector

Find length of bisector of a parallelogram if given side and angle ( L  ) :