QUADRILATERAL

, or Quadrilateral Figure, is a figure comprehended by four right lines; and having consequently also four angles, for which reason it is otherwise called a quadrangle.

The general term Quadrilateral comprehends these several particular species or figures, viz, the square, parallelogram, rectangle, rhombus, rhomboides, and trapezium.

If the opposite sides be parallel, the Quadrilateral is a parallelogram. If the parallelogram have its angles right ones, it is a rectangle; if oblique, it is an oblique one. The rectangle having all its sides equal, becomes a square; and the oblique parallelogram having all its sides equal, is a rhombus, but if only the opposites be equal, it is a rhomboides. All other forms of the Quadrilateral, are trapeziums, including all the irregular shapes of it.

The sum of all the four angles of any Quadrilateral, is equal to 4 right angles. Also, the two opposite angles of a Quadrilateral inscribed in a circle taken together, are equal to two right angles. And in this case the rectangle of the two diagonals, is equal to the sum of the two rectangles of the opposite sides. For the properties of the particular species of Quadrilaterals, see their respective names, Square, Rectangle, Parallelogram, Rhombus, Rhomboides, and Trapezium.