Geometry: Important Definitions
(quad means four, lateral means side).
Any foursided shape is a Quadrilateral.
But the sides have to be straight, and it has to be2dimensional. A quadrilateral is defined as any twodimensional, foursided shape that has four vertices with interior angles that equal 360 degrees. There are several quadrilateral variations that include parallelograms, rectangles, rhombuses, squares, trapezoids, and kites. Quadrilaterals
* Parallelogram – A parallelogram consists of two pairs of parallel sides. Opposite angles are equal. Rectangles, rhombuses, and squares are also considered parallelograms. * Rectangle – A rectangle has four sides; each side is a right angle (90°). * Rhombus – A rhombus has four sides, each one being of equal length and parallel to the opposite side. A rhombus with all right angles is a square. * Square – A square has four equal sides and four equal angles (90°). * Kite – A kite is a quadrilateral with two pairs of equal length, adjacent sides. * Trapezoid – A trapezoid is a quadrilateral that consists of 2 parallel sides. Quadrilateral Examples
Properties
* Four sides (edges)
* Four vertices (corners)
* The interior angles add up to 360 degrees:
Try drawing a quadrilateral, and measure the angles. They should add to 360° Types of Quadrilaterals
There are special types of quadrilateral:
Some types are also included in the definition of other types! For example a square, rhombus and rectangleare also parallelograms. See below for more details. Let us look at each type in turn:
The Rectangle
  
  means "right angle"
 and show equal sides
  
A rectangle is a foursided shape where every angle is a right angle (90°). Also opposite sides are parallel and of equal length.
The Rhombus
A rhombus is a foursided shape where all sides have equal length. Also opposite sides are parallel and opposite angles are equal. Another interesting thing is that the diagonals (dashed lines in second figure) meet in the middle at a right angle. In other words they "bisect" (cut in half) each other at right angles. The Square
  
  means "right angle"
  show equal sides
  
A square has equal sides and every angle is a right angle (90°) Also opposite sides are parallel.
A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length). The Parallelogram
A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "a" are the same, and angles "b" are the same). NOTE: Squares, Rectangles and Rhombuses are all Parallelograms! Example:
 A parallelogram with: * all sides equal and * angles "a" and "b" as right anglesis a square!
The Trapezoid (UK: Trapezium)

Trapezoid Isosceles Trapezoid
A trapezoid (called a trapezium in the UK) has a pair of opposite sides parallel. It is called an Isosceles trapezoid if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equal, as shown. A trapezium (UK: trapezoid) is a quadrilateral with NO parallel sides:  Trapezoid Trapezium
US: a pair of parallel sides NO parallel sides
UK: NO parallel sides a pair of parallel sides
The Kite
Hey, it looks like a kite. It has two pairs of sides. Each pair is made up of adjacent sides 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.
... and that's it for the special quadrilaterals.
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