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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).
The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle a appearing between sides a and b then its corresponding vertex angle v must appear between sides v and w.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled.. The terms "rhomboid" and "parallelogram" are often erroneously conflated with each other (i.e, when most people refer to a "parallelogram" they almost always mean a rhomboid, a specific subtype of parallelogram); however, while all rhomboids ...
It has two adjacent angles that are supplementary, that is, they add up to 180 degrees. The angle between a side and a diagonal is equal to the angle between the opposite side and the same diagonal. The diagonals cut each other in mutually the same ratio (this ratio is the same as that between the lengths of the parallel sides).
Transverse – intersecting at any angle, i.e. not parallel. Orthogonal (or perpendicular) – at a right angle (at the point of intersection). Elevation – along a curve from a point on the horizon to the zenith, directly overhead. Depression – along a curve from a point on the horizon to the nadir, directly below.
Vectors involved in the parallelogram law. In a normed space, the statement of the parallelogram law is an equation relating norms: ‖ ‖ + ‖ ‖ = ‖ + ‖ + ‖ ‖,.. The parallelogram law is equivalent to the seemingly weaker statement: ‖ ‖ + ‖ ‖ ‖ + ‖ + ‖ ‖, because the reverse inequality can be obtained from it by substituting (+) for , and () for , and then simplifying.
A kite with three 108° angles and one 36° angle forms the convex hull of the lute of Pythagoras, a fractal made of nested pentagrams. [22] The four sides of this kite lie on four of the sides of a regular pentagon, with a golden triangle glued onto the fifth side. [16] Part of an aperiodic tiling with prototiles made from eight kites