Quadrilateral Definition Quadrilateral Definition In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or edges) and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5sided), hexagon (6-sided) and so on. The origin of the word "quadrilateral" is the two Latin words quadri, a variant of four, and latus, meaning "side." Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also called crossed. Simple quadrilaterals are either convex or concave.The interior angles of a simple quadrilateral ABCD add up to 360 degrees of arc. This is a special case of the n-gon interior angle sum formula (n − 2) × 180°. In a crossed quadrilateral, the interior angles on either side of the crossing add up to 720°. All convex quadrilaterals tile the plane by repeated rotation around the midpoints of their edges.
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Convex quadrilaterals – parallelograms :- A parallelogram is a quadrilateral with two pairs of parallel sides. Equivalent conditions are that opposite sides are of equal length; that opposite angles are equal; or that the diagonals bisect each other. Parallelograms also include the square, rectangle, rhombus and rhomboid. Rhombus or rhomb: all four sides are of equal length. Equivalent conditions are that opposite sides are parallel and opposite angles are equal, or that the diagonals perpendicularly bisect each other. An informal description is "a pushedover square" (including a square). Rhomboid: a parallelogram in which adjacent sides are of unequal lengths and angles are oblique (not right angles). Informally: "a pushed-over rectangle with no right angles." Rectangle: all four angles are right angles. An equivalent condition is that the diagonals bisect each other and are equal in length. Informally: "a box or oblong" (including a square). Square (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are right angles. An equivalent condition is that opposite sides are parallel (a square is a parallelogram), that the diagonals perpendicularly bisect each other, and are of equal length. A quadrilateral is a square if and only if it is both a rhombus and a rectangle (four equal sides and four equal angles). Oblong: a term sometimes used to denote a rectangle which has unequal adjacent sides (i.e. a rectangle that is not a square).
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The sum of all the angles of the four sided figures (called quadrilaterals) is 360 degrees. We observe that the quadrilateral is the figure which is formed by the joining of two Triangles. When we join any two diagonals of the quadrilateral, it forms 2 triangles. Moreover we know that the sum of angles of the triangle is 180 degrees and so two triangles form 360 degrees. A kite is also a special type of quadrilateral, where we find that the opposite sides are not equal, but the pair of the adjacent sides of the kite is always equal, so we do not have the horizontal line of Symmetry, in kite as we have in the quadrilaterals square and the rectangles. A kite always has one vertical line of symmetry. Now we look at a parallelogram, which is he tilted form of the rectangle, but does not have a line of symmetry.
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