Parallelogram - patterns, perimeter, area

A parallelogram is a quadrilateral that has two pairs of parallel and equal sides. So, parallelograms are, for example, rectangles, squares and rhombuses.

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1. A parallelogram - what is it? Properties

A parallelogram is a special case of a trapezoid. It is characterized by the fact that its opposite sides are parallel and of equal length. The diagonals of the parallelogram intersect at half their length (but not always at right angles). The opposite angles in the parallelogram are of equal measure. The sum of the measures of the adjacent angles, i.e. those that lie on the same side, is 180 °.

A special case of a parallelogram is a rhombus with all sides of equal length, and a rectangle with four right angles and a square (all sides of equal length and four right angles).

2. Markings of the parallelogram

Parallelogram (Wikipedia)
  • a, b - the lengths of the sides of the parallelogram.
  • h - the height of the parallelogram, that is, the length of the segment connecting the two bases.
  • d1, d2 - lengths of the diagonals of the parallelogram;
  • φ - angle between the sides of the parallelogram;
  • o - angle between the diagonals of the parallelogram.

3. Parallelogram - surface area

Assuming that:

  • a, b - these are the two adjacent sides of the parallelogram,
  • α - is the angle between the sides,
  • d1, d2 - are the diagonals of the parallelogram,
  • γ - is the angle between the diagonals of the parallelogram.

The area of ​​the parallelogram is expressed by the formulas:

P = ah P = ab sinα

Area of ​​the parallelogram (Wikipedia)

4. Parallelogram - circumference

The formula for the perimeter of the parallelogram is:

Ob = 2a + 2b

Features of the parallelogram:

  • Opposite sides are of equal length and are parallel to each other.
  • The opposite angles are also of equal measure. The sum of the measures of angles lying on one side is 180 degrees.
  • The parallelogram has a center of symmetry.
  • The diagonals intersect at half their length.
  • You cannot write or describe a circle in a parallelogram (the exception is a rectangle).
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