# 4.1 Compare quadrilaterals for similarities and differences

 Page 1 / 2

## Compare quadrilaterals for similarities and differences

ACTIVITY 1

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.

ACTIVITY 2

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

Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
Got questions? Join the online conversation and get instant answers!