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Examples of cyclic quadrilaterals. In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.
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]
The orange and green quadrilaterals are congruent; the blue one is not congruent to them. Congruence between the orange and green ones is established in that side BC corresponds to (in this case of congruence, equals in length) JK, CD corresponds to KL, DA corresponds to LI, and AB corresponds to IJ, while angle ∠C corresponds to (equals) angle ∠K, ∠D corresponds to ∠L, ∠A ...
Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.
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 ...
All triangles can have an incircle, but not all quadrilaterals do. An example of a quadrilateral that cannot be tangential is a non-square rectangle . The section characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to be able to have an incircle.
Hutton's definitions in 1795 [4]. The ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and the last did not have two sets of parallel sides – a τραπέζια (trapezia [5] literally 'table', itself from τετράς (tetrás) 'four' + πέζα (péza) 'foot ...
Kites are examples of ex-tangential quadrilaterals. Parallelograms (which include squares, rhombi, and rectangles) can be considered ex-tangential quadrilaterals with infinite exradius since they satisfy the characterizations in the next section, but the excircle cannot be tangent to both pairs of extensions of opposite sides (since they are parallel). [4]