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Mathematics

Grade 9

Numbers

Module 3

Why all this fuss about pythagoras?

INVESTIGATION

1.1 Work in a group but start on your own by drawing three right–angled triangles of different shapes and sizes. Work as accurately as possible. It will be a lot easier if you use squared paper. Now work even more accurately and measure the three sides of each triangle to the nearest millimetre. Complete the first three rows of the table. Now use your calculator to complete the rest of the table.

SYMBOL TRIANGLE A TRIANGLE B TRIANGLE C
Length of the shortest side a .................... .................... ....................
Length of the medium triangle b .................... .................... ....................
Length of the longest side c .................... .................... ....................
Square of the length of the shortest side a 2 .................... .................... ....................
Square of the length of the medium side b 2 .................... .................... ....................
Sum of the two squares above a 2 + b 2 .................... .................... ....................
Square of the length of the longest side c 2 .................... .................... ....................

1.2 There should be something interesting about the shaded cells of the table. In your group write down carefully what you notice and (if you can) why it happens.

2. Take three lines:

  • The three given lines can be used to form a right–angled triangle.

Cutting–out:

2.1 Can the three given squares be used to form a triangle?

3 Write a neat summary of the results of the investigation.

end of INVESTIGATION

The Theorem of Pythagoras goes:

  • In a right–angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

The importance of the Theorem of Pythagoras is that we use it in two ways: Firstly, if we know that a triangle is right angled, then we can say something very important about its sides. Secondly, if we know that the three sides of a triangle have a certain relationship with each other, then we also know that the triangle must be right–angled.

CLASS WORK

1 We label triangles as follows:

  • Refer to the sketch alongside.
  • The three vertices (corners) get capital letters. (A, B and C).
  • The sides can be named as the two vertices betweenwhich the side lies (AB, BC and AC), or we can uselowercase letters, each corresponding to the vertexopposite the side (a, b and c).
  • At the moment we are dealing with right–angled triangles, but all triangles are labelled the same way.
  • We also use the same letter to refer both to the name of a side and to its length.
  • E.g. PR = 3,5cm or r = 5cm.ΔPRS means: triangle PRS

REMEMBER always to use a ruler for good sketches!

  • In the following exercise the first problem is always an example.

2 Problem : AEH has a right angle at H.AH = 6cm and EH = 8cm.Draw a sketch (not accurate) of the triangle and use the Theorem of Pythagoras to calculate the length of side AE.

Solution : Because we know that the triangle has a rightangle, we are allowed to say that AE 2 = AH 2 + EH 2 (or: h 2 = e 2 + a 2 )

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
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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