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Mathematics

Grade 9

Quadrilaterals, perspective drawing,transformations

Module 22

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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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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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