A quadrilateral has four-sides, it is 2-dimensional (a level shape), closed (the lines sign up with up), and also has straight sides.

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(Also see this on interactive Quadrilaterals)

Properties

A quadrilateral has:

four sides (edges) 4 vertices (corners) inner angles that add to 360 degrees:

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Try illustration a quadrilateral, and also measure the angles. Lock should include to 360°

Types the Quadrilaterals

There are special species of quadrilateral:

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Some species are additionally included in the definition of other types! For example a square, rhombus and rectangle are likewise parallelograms. See below for more details.

Let us look in ~ each form in turn:

The Rectangle

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the little squares in each edge mean "right angle"

A rectangle is a four-sided form where every angle is a appropriate angle (90°).

Also opposite sides space parallel and of equal length.

The Square

the tiny squares in each corner mean "right angle"

A square has actually equal sides (marked "s") and also every angle is a right angle (90°)

Also the contrary sides space parallel.

A square likewise fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

The Rhombus

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A rhombus is a four-sided form where every sides have actually equal size (marked "s").

Also the opposite sides space parallel and also opposite angles are equal.

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Another amazing thing is the the diagonals (dashed lines) satisfy in the center at a right angle. In various other words they "bisect" (cut in half) each various other at ideal angles.

A rhombus is sometimes referred to as a rhomb or a diamond.

The Parallelogram

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A parallelogram has opposite sides parallel and equal in length. Likewise opposite angles space equal (angles "A" space the same, and also angles "B" space the same).

NOTE: Squares, Rectangles and also Rhombuses space all Parallelograms!


Example:

A parallelogram with:

all sides same andangles "A" and "B" as appropriate angles

is a square!


The Trapezoid (UK: Trapezium)

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Trapezoid
Isosceles Trapezoid

A trapezoid (called a trapezium in the UK) has actually a pair that opposite political parties parallel.

And a trapezium (called a trapezoid in the UK) is a quadrilateral through NO parallel sides:

TrapezoidTrapezium
In the US:a pair of parallel sidesNO parallel sides
In the UK:NO parallel sidesa pair the parallel sides
(the US and UK interpretations are swapped over!)

An Isosceles trapezoid, as presented above, has actually left and right political parties of equal size that sign up with to the base at equal angles.

The Kite

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Hey, it looks like a dragon (usually).

It has two pairs that sides:

Each pairis make of 2 equal-length sides that join up.

Also:

the angles whereby the 2 pairs fulfill are equal.the diagonals, shown as dashed present above, meet at a right angle.one the the diagonals bisects (cuts equally in half) the other.

... And that"s it for the special quadrilaterals.

Irregular Quadrilaterals

The only continuous (all sides equal and all angles equal) quadrilateral is a square. For this reason all other quadrilaterals are irregular.

The "Family Tree" Chart

Quadrilateral definitions are inclusive.


Example: a square is additionally a rectangle.

So we include a square in the definition of a rectangle.

(We don"t say "Having every 90° angles makes it a rectangle other than when all sides space equal climate it is a square.")


This might seem odd, together in daily life us think of a square as not gift a rectangle ... Yet in math it is.

Using the chart below we deserve to answer such questions as:

Is a Square a form of Rectangle? (Yes) Is a Rectangle a kind of Kite? (No)

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Complex Quadrilaterals

Oh Yes! as soon as two sides cross over, we call it a "Complex" or "Self-Intersecting" quadrilateral, favor these:

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They still have actually 4 sides, yet two sides cross over.

Polygon

A square is a polygon. In fact it is a 4-sided polygon, similar to a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on.

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Play with Them

Now the you recognize the various types, you can play through the interaction Quadrilaterals.

Other Names

A quadrilateral deserve to sometimes be called:


a Quadrangle ("four angles"), so that sounds prefer "triangle" a Tetragon ("four polygon"), so the sounds favor "pentagon", "hexagon", etc.
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polygons Interactive Quadrilaterals ideal Angle Parallel parallel In any kind of Quadrilateral Geometry Index