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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).
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four straight sides of equal length and four equal angles (90-degree angles, π /2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adjacent sides.
The cyclic quadrilaterals may equivalently defined as the quadrilaterals in which two opposite angles are supplementary (they add to 180°); if one pair is supplementary the other is as well. [9] Therefore, the right kites are the kites with two opposite supplementary angles, for either of the two opposite pairs of angles.
The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
Consecutive interior angles are the two pairs of angles that: [4] [2] have distinct vertex points, lie on the same side of the transversal and; are both interior. Two lines are parallel if and only if the two angles of any pair of consecutive interior angles of any transversal are supplementary (sum to 180°).
Many results about plane figures are proved, for example, "In any triangle, two angles taken together in any manner are less than two right angles." (Book I proposition 17) and the Pythagorean theorem "In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle ...
Right kite: a kite with two opposite right angles. It is a type of cyclic quadrilateral. Harmonic quadrilateral: a cyclic quadrilateral such that the products of the lengths of the opposing sides are equal. Bicentric quadrilateral: it is both tangential and cyclic. Orthodiagonal quadrilateral: the diagonals cross at right angles.
For example, two rhombi both having common side a (and, as for all rhombi, both having a right angle between the diagonals), but one having a smaller acute angle than the other, have different areas (the area of the former approaching zero as the acute angle approaches zero). If squares are erected outward on the sides of any quadrilateral ...