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Grade 9

Quadrilaterals, perspective drawing,transformations

Module 22

Compare quadrilaterals for similarities and differences


To compare quadrilaterals for similarities and differences

[LO 3.4]

1. Comparisons

For the next exercise you can form small groups. You are given pairs of quadrilaterals, which you have to compare. Write down in which ways they are alike and in which ways they are different. If you can say exactly by what process you can change the one into the other, then that will show that you have really understood them. For example, look at the question on parallel sides at the end of section 3 above.

Each group should work with at least one pair of shapes. When you work with a kite, you should consider both versions of the kite.

  • Rhombus and square
  • Trapezium and parallelogram
  • Square and rectangle
  • Kite and rhombus
  • Parallelogram and kite
  • Rectangle and trapezium

If, in addition, you would like to compare a different pair of quadrilaterals, please do so!

1. Definitions

A very short, but accurate, description of a quadrilateral using the following characteristics, is a definition . This definition is unambiguous, meaning that it applies to one shape and one shape only, and we can use it to distinguish between the different types of quadrilateral.

The definitions are given in a certain order because the later definitions refer to the previous definitions, to make them shorter and easier to understand. There is more than one set of definitions, and this is one of them.

  • A quadrilateral is a plane (flat) figure bounded by four straight lines called sides.
  • A kite is a quadrilateral with two pairs of equal adjacent sides.
  • A trapezium is a quadrilateral with one pair of parallel opposite sides.
  • A parallelogram is a quadrilateral with two pairs of parallel opposite sides.
  • A rhombus is a parallelogram with equal adjacent sides.
  • A square is a rhombus with four equal internal angles.
  • A rectangle is a parallelogram with four equal internal angles.


To develop formulas for the area of quadrilaterals intuitively

[LO 3.4]

Calculating areas of plane shapes .

  • Firstly, we will work with the areas of triangles. Most of you know the words “half base times height”. This is the formula for the area of a triangle, where we use A for the area , h for the height and b for the base .
  • Area = ½ × base × height; A = ½ bh ; A = are various forms of the formula.
  • But what is the base ? And what is the height ? The important point is that the height and the base make up a pair: the base is not any old side, and the height is not any old line.

  • The height is a line that is perpendicular to the side that you choose as the base. Refer to the sketches above. The base and its corresponding height are drawn as darker lines. Below are three more examples showing the base/height pairs.
  • Take two other colours, and in each of the above six triangles draw in the two other matching pairs of base/height, each pair in its own colour. Then do the following exercise:

Pick one of the triangles above, and calculate its area three times. Measure the lengths with your ruler, each time using another base/height pair. Do you find that answers agree closely? If they don’t, measure more carefully and try again.

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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