![]() (Because then the opposite sides are parallel.) A simple quadrilateral with two pairs of equal opposite sides is a parallelogram. And not to forget, every simple quadrilateral tiles the plane.Ī simple quadrilateral with two pairs of equal opposite angles is a parallelogram. In particular, a parallelogram with equal diagonals is necessarily a rectangle. Orthodiagonal or inscriptible parallelogram is a rhombus cyclic parallelogram is a rectangle. Rhombus, Square, Rectangle, Parallelogram Rhombus, Square, Rectangle, Parallelogram, Trapezoid Here is a list of all the properties of quadrilaterals that we have mentioned along with the classes of the quadrilaterals that possess those properties: For, I'd like to think of a square as a rhombus with right angles, or as a rectangle with all four sides equal. My preference is with the inclusive approach. Similarly, a square may or may not be a rectangle or a rhombus. In the former case, parallelogram is a trapezoid, in the latter, it is not. For example, trapezoid may be defined inclusively as a quadrilateral with a pair of parallel opposite sides, or exclusively as a quadrilateral with exactly one such pair. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.Īs in the classification of triangles, the definitions may be either inclusive or exclusive. This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which, too, is not overly difficult if you first get an isosceles trapezoid.) With these props, it's a simple matter to observe every single kind of quadrilateral, with a possible exception of bicentric. You can display its diagonals, angle bisectors and the perpendicular bisectors of its sides. In the applet, one can drag the vertices and the sides of the quadrilateral. The applet below illustrates the properties of various quadrilaterals. The diagram below (which is a modification of one from ) summarize the relationship between various kinds of quadrilaterals: A quadrilateral, both cyclic and inscriptible, is bicentric. ![]() ![]() If a quadrilateral admits an incircle that touches all four of its sides (or more generally, side lines), it is known as inscriptible. In this case, the quadrilateral is known as circumscritptible or, simpler, cyclic. The four vertices of a quadrilateral may be concyclic, i.e., lie on the same circle. A square and a rhombus are also particular cases of this class. quadrilaterals with perpendicular diagonals. Kite and dart are examples of orthodiagonal quadrilaterals, i.e. However, if the kite is concave, a dart is a more appropriate term. A quadrilateral with two separate pairs of equal adjacent sides is commonly called a kite. A trapezoid, in which the non-parallel sides are equal in length, is called isosceles. If only one pair of opposite sides is required to be parallel, the shape is a trapezoid. A quadrilateral with the opposite side lines parallel is known as a parallelogram. In a square, rectangle, or rhombus, the opposite side lines are parallel. the one with all sides equal, is a rhombus. the one with all angles equal is a rectangle. It follows that, in a square, all angles measure 90°. Angles in any quadrilateral add up to 360°. Starting with the most regular quadrilateral, namely, the square, we shall define other shapes by relaxing its properties.Ī square is a quadrilateral with all sides equal and all angles also equal. The shapes of elementary geometry are invariably convex. The point of intersection of the sides is not considered a vertex of the quadrilateral. A quadrilateral that is not simple is also known as self-intersecting to indicate that a pair of his non-adjacent sides intersect. So that two non-adjacent sides do not cross. In either case, the quadrilateral is simple, which means that the four sides of the quadrilateral only meet at the vertices, two at a time. The seldom used term quadrangle has exactly the same meaning as quadrilateral, however the two related terms - complete quadrangle and complete quadrilateral - describe essentially different configurations.Ī quadrilateral may be convex or concave (see the diagram below.) A quadrilateral that is concave has an angle exceeding 180 o. Although we use words like pentagon and polygon, the term quadrilateral has completely replaced tetragon. The Latin term is a partial translation of Greek tetragon, literally "four angles," since a closed figure with four angles also has four sides. Quadrilateral (noun, adjective): the first element is from Latin quadri- "four" from the Indo-European root k wetwer- "four." The second element is from Latin latus, stem later-, "side," of unknown prior origin. Quadrilateral is a geometric shape that consists of four points ( vertices) sequentially joined by straight line segments ( sides).
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