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

You are watching: Can a rectangle be a square


(Also see this on interactive Quadrilaterals)

Properties

A quadrilateral has:

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

*

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

Types that Quadrilaterals

There space special varieties of quadrilateral:

*

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

Let united state look in ~ each form in turn:

The Rectangle

*
the small squares in each edge mean "right angle"

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

Also opposite sides space parallel and of equal length.

The Square

the little squares in each corner mean "right angle"

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

Also the contrary sides are parallel.

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

The Rhombus

*

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

Also opposite sides room parallel and opposite angles are equal.

*

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

A rhombus is sometimes called a rhomb or a diamond.

The Parallelogram

*

A parallelogram has actually opposite sides parallel and equal in length. Also opposite angles room equal (angles "A" are the same, and 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 right angles

is a square!


The Trapezoid (UK: Trapezium)

*
*

Trapezoid
Isosceles Trapezoid

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

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

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

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

The Kite

*

Hey, that looks prefer 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 fulfill are equal.the diagonals, presented as dashed present above, accomplish at a best angle.one that the diagonals bisects (cuts equally in half) the other.

... And that"s it because that the distinct quadrilaterals.

Irregular Quadrilaterals

The only regular (all sides equal and all angles equal) quadrilateral is a square. Therefore all other quadrilaterals are irregular.

The "Family Tree" Chart

Quadrilateral definitions are inclusive.


Example: a square is also a rectangle.

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

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


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

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

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

*

Complex Quadrilaterals

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

*

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

Polygon

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

See more: Is Lovely Bones A True Story ? Is My Lovely Bones A True Story

Play with Them

Now that you understand the various types, you have the right to play v the interaction Quadrilaterals.

Other Names

A quadrilateral have the right to sometimes be called:


a Quadrangle ("four angles"), so it sounds favor "triangle" a Tetragon ("four polygon"), so the sounds choose "pentagon", "hexagon", etc.
621,622,623,624,763,764, 2128, 2129, 3230, 3231
polygon Interactive Quadrilaterals ideal Angle Parallel parallelogram In any type of Quadrilateral Geometry Index