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  2. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8] A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. [9]

  3. Cyclic quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Cyclic_quadrilateral

    Usually the quadrilateral is assumed to be convex, but there are also crossed cyclic quadrilaterals. The formulas and properties given below are valid in the convex case. The word cyclic is from the Ancient Greek κύκλος (kuklos), which means "circle" or "wheel". All triangles have a circumcircle, but not all

  4. Bretschneider's formula - Wikipedia

    en.wikipedia.org/wiki/Bretschneider's_formula

    Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals e and f to give [2] [3]

  5. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities

  6. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    All of the area formulas for general convex quadrilaterals apply to parallelograms. Further formulas are specific to parallelograms: Further formulas are specific to parallelograms: A parallelogram with base b and height h can be divided into a trapezoid and a right triangle , and rearranged into a rectangle , as shown in the figure to the left.

  7. Brahmagupta's formula - Wikipedia

    en.wikipedia.org/wiki/Brahmagupta's_formula

    This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.

  8. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Van Aubel's theorem (quadrilaterals) Van der Waerden's theorem (combinatorics) Van Schooten's theorem (Euclidean geometry) Van Vleck's theorem (mathematical analysis) Vantieghems theorem (number theory) Varignon's theorem (Euclidean geometry) Vieta's formulas ; Vietoris–Begle mapping theorem (algebraic topology) Vinogradov's theorem (number ...

  9. Isosceles trapezoid - Wikipedia

    en.wikipedia.org/wiki/Isosceles_trapezoid

    Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...