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MATHS PROJECT Quadrilaterals

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Definition

A plane figure bounded by four line segments AB,BC,CD and DA is called a quadrilateral.

In geometry, a quadrilateral is a polygon with four

sides and four vertices. Sometimes, the term quadrangle is used, for etymological symmetry with triangle, and sometimes tetragon for consistence with pentagon.

There are over 9,000,000 quadrilaterals. Quadrilaterals are either simple (not self-intersecting) or complex (self-intersecting). Simple quadrilaterals are either convex or concave.

Is a square a rectangle?

Some people define categories exclusively, so that a rectangle is a quadrilateral with four right angles that is not a square. This is appropriate for everyday use of the words, as people typically use the less specific word only when the more specific word will not do. Generally a rectangle which isn't a square is an oblong.

But in mathematics, it is important to define categories inclusively, so that a square is a rectangle. Inclusive categories make statements of theorems shorter, by eliminating the need for tedious listing of cases. For example, the visual proof that vector addition is commutative is known as the "parallelogram diagram". If categories were exclusive it would have to be known as the "parallelogram (or rectangle or rhombus or square) diagram"!

Kite

It has two pairs of sides.

Each pair is made up of adjacent sides (the sides meet) that are equal in length. The angles are equal where the pairs meet. Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other.