Types of Quadrilaterals

Special types of Quadrilaterals : Special types of Quadrilaterals -Diviz Goyal

Quadrilaterals : Quadrilaterals a quadrilateral is a polygon with four sides or edges and four vertices or corners. Quadrilaterals are either simple (not self-intersecting) or complex (self-intersecting). Simple quadrilaterals are either convex or concave.

Types of quadrilaterals : Types of quadrilaterals quadrilaterals are further classified as follows: Trapezium Parallelogram Rhombus Rectangle Square Cyclic Quadrilateral Tangential Quadrilateral

Trapezium Or Trapezoid : Trapezium Or Trapezoid a trapezium is a quadrilateral that has at least one pair of parallel lines for sides. Length of sides of trapezium can be different. A quadrilateral is a trapezoid if and only if it contains two adjacent angles that are supplementary, that is, they add up to one straight angle of 180 degrees.

Parallelogram : Parallelogram a parallelogram is a quadrilateral with two sets of parallel sides. The opposite sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are congruent. The three-dimensional counterpart of a parallelogram is a parallelepiped.

Properties of llgm : Properties of llgm The area, A, of a parallelogram is A = BH, where B is the base of the parallelogram and H is its height. The area of a parallelogram is twice the area of a triangle created by one of its diagonals. The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides. The diagonals of a parallelogram bisect each other. Opposite sides of a parallelogram are equal. Opposite angles of a parallelogram are equal. Each diagonal bisects the parallelogram into two congruent triangles.

Rhombus : Rhombus In geometry, a rhombus or rhomb is an equilateral quadrilateral. In other words, it is a four-sided polygon in which every side has the same length. In any rhombus, opposite sides are parallel. Thus, the rhombus is a special case of the parallelogram. One analogy holds that the rhombus is to the parallelogram as the square is to the rectangle.

Rectangle : Rectangle In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. a rectangle has two pairs of parallel sides; that is, a rectangle is a parallelogram. The area of a rectangle is the product of its length and its width; in symbols, A = lw.

Square : Square A square is a special kind of rectangle where all four sides have equal length; that is, a square is both a rectangle and a rhombus. A square is a special case of a rectangle as it has four right angles and equal parallel sides. The area of a square is the product of the length of its sides. The perimeter of a square whose sides have length t is P = 4t Each angle in a square is equal to 90 degrees, or a right angle.

Non-Euclidean geometry : Non-Euclidean geometry In non-Euclidean geometry, squares are more generally polygons with 4 equal sides and equal angles. In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle. In hyperbolic geometry, squares with right angles do not exist. Rather, squares in hyperbolic geometry have angles of less than right angles. Larger squares have smaller angles.

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