The parallelogram is the convex quadrilateral with opposite parallel sides.
Properties
- Opposite sides are congruent two by two.
- Opposite angles are congruent and adjacent angles are additional (their sum is equal to 180 degrees).
- Its diagonals are cut into congruent segments (“halved”).
- The area A of a parallelogram is A = b • h, where b is the length of a side and h is the height corresponding to this side.
- The area of a parallelogram is equal to twice the area of the triangle formed by two adjacent sides and the diagonal opposite them.
- The area of a parallelogram is equal to the product of the lengths of two adjacent sides and the sinus of one of the angles of the parallelogram.
Mutual theorems
- If in a convex quadrilateral the opposite sides are congruent two by two, then the quadrilateral is a parallelogram.
- If in a convex quadrilateral two opposite sides are parallel and congruent, then the quadrilateral is a parallelogram.
- If in a convex quadrilateral the opposite angles are congruent, then the quadrilateral is a parallelogram.
- If in a convex quadrilateral the diagonals have the same means, then the quadrilateral is a parallelogram.
