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The centers of four squares all constructed either internally or externally on the sides of a parallelogram are the vertices of a square. [ 8 ] If two lines parallel to sides of a parallelogram are constructed concurrent to a diagonal, then the parallelograms formed on opposite sides of that diagonal are equal in area.
The second is a link to the article that details that symbol, using its Unicode standard name or common alias. (Holding the mouse pointer on the hyperlink will pop up a summary of the symbol's function.); The third gives symbols listed elsewhere in the table that are similar to it in meaning or appearance, or that may be confused with it;
The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases. A scalene trapezoid is a trapezoid with no sides of equal measure, [4] in contrast with the special cases below.
A square is a rhombus with all angles equal. [1] A square is a parallelogram with one right angle and two adjacent equal sides. [1] A square is a quadrilateral with four equal sides and four right angles; that is, it is a quadrilateral that is both a rhombus and a rectangle [1]
The first property implies that every rhombus is a parallelogram. 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 ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
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.