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

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Properties

A square has:

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

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

Types that Quadrilaterals

There are special types of quadrilateral:

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Some varieties are additionally included in the meaning of other types! For example a square, rhombus and also rectangle are also parallelograms. See below for much more details.

Let us look at each kind in turn:

The Rectangle

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the small squares in each corner mean "right angle"

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

Also the opposite sides space parallel and also of same length.

The Square

the small squares in each corner mean "right angle"

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

Also opposite sides room parallel.

A square likewise fits the an interpretation 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 every sides have actually equal size (marked "s").

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

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Another interesting thing is that the diagonals (dashed lines) satisfy in the middle at a right angle. In 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 actually opposite sides parallel and also equal in length. Also opposite angles room equal (angles "A" space the same, and also angles "B" space the same).

NOTE: Squares, Rectangles and Rhombuses room all Parallelograms!


Example:

A parallelogram with:

all sides equal andangles "A" and "B" as best angles

is a square!


The Trapezoid (UK: Trapezium)

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Trapezoid
Isosceles Trapezoid

A trapezoid (called a trapezium in the UK) has a pair of 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 of parallel sidesNO parallel sides
In the UK:NO parallel sidesa pair that parallel sides
(the US and UK interpretations are swapped over!)

An Isosceles trapezoid, as presented above, has actually left and also right sides of equal size that join to the base at same angles.

The Kite

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Hey, the looks choose a dragon (usually).

It has two pairs of sides:

Each pairis do of two equal-length sides that join up.

Also:

the angles where the 2 pairs accomplish are equal.the diagonals, presented as dashed lines above, accomplish at a ideal angle.one of the diagonals bisects (cuts same in half) the other.

... And also that"s it for the distinct quadrilaterals.

Irregular Quadrilaterals

The only regular (all sides equal and all angles equal) square is a square. For this reason all other quadrilaterals space irregular.

The "Family Tree" Chart

Quadrilateral meanings are inclusive.


Example: a square is likewise a rectangle.

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

(We don"t to speak "Having every 90° angles provides it a rectangle other than when every sides room equal then it is a square.")


This might seem odd, as in daily life we think that a square together not being a rectangle ... But in math it is.

Using the chart listed below we deserve to answer such inquiries as:

Is a Square a form 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 speak to it a "Complex" or "Self-Intersecting" quadrilateral, choose these:

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

Polygon

A quadrilateral 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 through Them

Now that you know the various types, you deserve to play v the interaction Quadrilaterals.

Other Names

A quadrilateral deserve to sometimes it is in called:


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