A quadrilateral has four-sides, the is 2-dimensional (a flat shape), closed (the lines join up), and also has straight sides.

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(Also view this on interaction Quadrilaterals)

Properties

A square has:

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

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Try drawing a quadrilateral, and measure the angles. They should add to 360°

Types of Quadrilaterals

There are special types of quadrilateral:

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Some varieties are also included in the an interpretation of various other types! For example a square, rhombus and rectangle are additionally parallelograms. See listed below for an ext details.

Let us look in ~ each kind in turn:

The Rectangle

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the small squares in each edge mean "right angle"

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

Also the opposite sides room parallel and of equal length.

The Square

the small squares in each corner mean "right angle"

A square has equal political parties (marked "s") and every edge is a best angle (90°)

Also the contrary sides are parallel.

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

The Rhombus

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

Also opposite sides room parallel and also opposite angles space equal.

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Another interesting thing is that the diagonals (dashed lines) satisfy in the center at a right angle. In other words castle "bisect" (cut in half) each 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 actually opposite sides parallel and also equal in length. Also opposite angles are equal (angles "A" space the same, and also angles "B" room the same).

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


Example:

A parallelogram with:

all sides equal andangles "A" and also "B" as ideal 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 sides parallel.

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

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

An Isosceles trapezoid, as displayed above, has left and also right sides of equal length that sign up with to the base at equal angles.

The Kite

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Hey, the looks favor a kite (usually).

It has actually two pairs the sides:

Each pairis made of two equal-length political parties that sign up with up.

Also:

the angles where the two pairs accomplish are equal.the diagonals, presented as dashed currently above, accomplish at a appropriate angle.one of the diagonals bisects (cuts equally in half) the other.

... And also that"s it because that the one-of-a-kind quadrilaterals.

Irregular Quadrilaterals

The only continuous (all sides equal and also all angles equal) quadrilateral is a square. Therefore all various other quadrilaterals room irregular.

The "Family Tree" Chart

Quadrilateral interpretations are inclusive.


Example: a square is additionally a rectangle.

So us include a square in the meaning of a rectangle.

(We don"t to speak "Having all 90° angles renders it a rectangle other than when every sides are equal climate it is a square.")


This might seem odd, together in everyday life us think the a square together not being a rectangle ... But in math it is.

Using the chart listed below we have the right to answer such concerns as:

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

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Complex Quadrilaterals

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

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They still have 4 sides, however two sides cross over.

Polygon

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

See more: Shuckling: Why Do Orthodox Jews Rock When They Pray ? Why Do Jews Rock When They Pray

Play with Them

Now the you recognize the different types, you can play with the interactive Quadrilaterals.

Other Names

A quadrilateral can sometimes be called:


a Quadrangle ("four angles"), so that sounds like "triangle" a Tetragon ("four polygon"), so that sounds choose "pentagon", "hexagon", etc.
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polygons Interactive Quadrilaterals right Angle Parallel parallelogram In any Quadrilateral Geometry Index