Lesson Difference between parallelogram,rectangle, square, rhombus and trapezoid

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Source code of 'Difference between parallelogram,rectangle, square, rhombus and trapezoid'

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In this lesson we are going to deal with definition of parallelogram, rectangles, square, rhombus and trapezoid. Further we are going to understand how to distinguish between each of them and their properties.

<A HREF=http://www.algebra.com/algebra/homework/Rectangles/Parallelogram.wikipedia>Parallelogram</A>

{{{drawing( 160, 160, -10, 10, -10, 10, line( -6, -6,4,-6) , line( -6, -6,-2,2), line( -2, 2,8,2) , line( 8, 2,4,-6),line( -6, -6,8,2) ,line( -2, 2,4,-6) ,locate( -6.5,-6.5,A),locate( 4.5,-6.5,B),locate( 8.5,3.5,C),locate(-2.5,4,D),locate(-0,-2.4,O))}}}

Parallelogram is a <A HREF=The-Quadrangle.wikipedia>quadrangle</A>, opposite sides of which are two-by-two parallel.

Any two opposite sides of a parallelogram are called bases, a distance between them is called a height.

<A HREF=http://www.algebra.com/algebra/homework/Rectangles/Rectangle.wikipedia>Rectangle</A>

{{{drawing( 160, 160, -10, 10, -10, 10, line( -6, -6,4,-6) , line( -6, -6,-6,1.5), line( -6, 1.5,4,1.5) , line( 4, 1.5,4,-6) ,locate( -6.5,-6.5,A),locate( 4.5,-6.5,B),locate( 4.5,2.5,C),locate(-7,3,D))}}}

If all <A HREF=Introduction-and-Properties-of-Angles.lesson>angles</A> of parallelogram are 90 degree then it can either be a rectangle or a square.

To distinguish a rectangle from square following property should be kept in mind:

1. Only opposite sides of a rectangle are equal unlike square which has all sides equal.

To distinguish a rectangle from rhombus following property should be kept in mind:

2. Each angle of rectangle is 90 degrees unlike rhombus where angles are not equal to 90 degrees.

<A HREF=http://www.algebra.com/~pavlovd/wiki/Rhombus>Rhombus</A>

{{{drawing( 160, 160, -10, 10, -10, 10, line( -6, -6,4,-6) , line( -6, -6,-1.29,3.42), line( -1.29, 3.42,8.71,3.42) , line( 8.71,3.42,4,-6),line( -6, -6,8.71,3.42) ,line( -1.29,3.42,4,-6) ,locate( -6.5,-6.5,A),locate(4.5,-6.5,B),locate( 9,4.5,C),locate(-2.3,5.3,D))}}}

If all sides of parallelogram are equal but angles are not equal to 90 degrees, then this parallelogram is called a rhombus.

Rhombus and square have all sides equal, to distinguish a rhombus from square following property should be kept in

Each angle of square has to be 90 degrees unlike rhombus.

To distinguish a rectangle from rhombus following property should be kept in mind:

2. Each angle of rectangle has to be 90 degrees unlike rhombus.

3. Unlike rhombus only opposite sides of rectangle are equal.

<A HREF=http://www.algebra.com/algebra/homework/Rectangles/Square_%28geometry%29.wikipedia>Square</A>

{{{drawing( 160, 160, -10, 10, -10, 10, line( -6, -6,4,-6) , line( -6, -6,-6,4), line( -6, 4,4,4) , line( 4, 4,4,-6) ,locate( -6.5,-6.5,A),locate( 4.5,-6.5,B),locate( 4.5,4.5,C),locate(-7.5,5,D))}}}

A square is a parallelogram with right angles and equal sides. A square is a particular case of a rectangle and a rhombus simultaneously. So, it shows both the properties of rhombus and rectangle simultaneously.

Square can be differentiated from a rectangle and rhombus due to following properties.

1. Unlike rectangle square needs to have all its sides equal.

2. Unlike rhombus square needs to have all angles equal to 90 degree.

<A HREF=Trapezoid.wikipedia>Trapezoid</A>

{{{drawing( 160, 160, -10, 10, -10, 10, line( -6, -6,4,-6) , line( -6, -6,-4,4), line( -4,4,2,4) , line( 2, 4,4,-6) ,locate( -6.5,-6.5,A),locate( 4.5,-6.5,B),locate( 2.5,4.5,C),locate(-5.5,5,D))}}}

A quadrangle which has only one of the two opposite sides as parallel is called a Trapezoid.
The other opposite sides need not be parallel. If both pair of opposite sides of a trapezoid are parallel then it becomes a parallelogram. The trapezoid does not follow the basic properties of a parallelogram.

For further reading into parallelogram refer to this <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/types-of-parallelogram.lesson>lesson</A>