Search results
Results From The WOW.Com Content Network
A simple (non-self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true: [2] [3] Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure. The diagonals bisect each other.
An equivalent condition is that opposite sides are parallel (a square is a parallelogram), and that the diagonals perpendicularly bisect each other and are of equal length. A quadrilateral is a square if and only if it is both a rhombus and a rectangle (i.e., four equal sides and four equal angles).
An antiparallelogram. In geometry, an antiparallelogram is a type of self-crossing quadrilateral.Like a parallelogram, an antiparallelogram has two opposite pairs of equal-length sides, but these pairs of sides are not in general parallel.
Twice the length of the bimedian connecting the midpoints of two opposite sides equals the sum of the lengths of the other sides. [16]: p. 31 Additionally, the following properties are equivalent, and each implies that opposite sides a and b are parallel: The consecutive sides a, c, b, d and the diagonals p, q satisfy the equation [16]: Cor.11
An arbitrary quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A ...
A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of the squares of the diagonals (the parallelogram law).
A square is a special case of a rhombus (equal sides, opposite equal angles), a kite (two pairs of adjacent equal sides), a trapezoid (one pair of opposite sides parallel), a parallelogram (all opposite sides parallel), a quadrilateral or tetragon (four-sided polygon), and a rectangle (opposite sides equal, right-angles), and therefore has all ...
For the general quadrilateral (with four sides not necessarily equal) Euler's quadrilateral theorem states + + + = + +, where is the length of the line segment joining the midpoints of the diagonals. It can be seen from the diagram that x = 0 {\displaystyle x=0} for a parallelogram, and so the general formula simplifies to the parallelogram law.