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Mathematics

Grade 8

Rational numbers, circles and triangles

Module 14

Classifying and constructing triangles

Activity 1

Classifying triangles, discovering important theorems about triangles and constructing triangles

[lo 3.1, 3.3, 3.4, 4.2.1]

  • By the end of this learning unit, you will be able to do the following:
  • understand how important the use of triangles is in everyday situations;
  • explain how to find the unknown sides of a right-angled triangle (Pythagoras);
  • calculate the area of a triangle;
  • enjoy the action in geometry;
  • use mathematical language to convey mathematical ideas, concepts, generalisations and mental processes.

1. When you classify triangles you can do it according to the angles or according to the sides.

1.1 Classification on the basis of the angles of a triangle:Are you able to complete the following?

a) Acute-angled triangles are triangles with

b) Right-angled triangles have

c) Obtuse-angled triangles have

1.2 Classification on the basis of the sides of the triangle:Are you able to complete the following?

a) An isosceles triangle has

b) An equilateral triangle has

c) A scalene triangle's

2. Are you able to complete the following theorems about triangles? Use a sketch to illustrate each of the theorems graphically.

THEOREM 1:

  • The sum of the interior angles of any triangle is.........................

Sketch:

THEOREM 2:

  • The exterior angle of a triangle is

Sketch:

3. Constructing triangles:

  • Equipment: compasses, protractor, pencil and ruler

Remember this:

  • Begin by drawing a rough sketch of the possible appearance.
  • Begin by drawing the base line.

3.1 Construct Δ size 12{Δ} {} PQR with PQ = 7 cm, PR = 5 cm and P ˆ size 12{ { hat {P}}} {} = 70°.

a) Sketch:

b) Measure the following:

1. QR = ........ 2. R ˆ size 12{ { hat {R}}} {} = ........ 3. Q ˆ size 12{ { hat {Q}}} {} = ........ 4. P ˆ + Q ˆ + R ˆ = size 12{ { hat {P}}+ { hat {Q}}+ { hat {R}}={}} {} ........

3.2 Construct Δ size 12{Δ} {} KLM , an equilateral triangle. KM = 40 mm, KL = LM and K ˆ size 12{ { hat {K}}} {} = 75°.Indicate the sizes of all the angles in your sketch.

Sketch:

Activity 2

Discovering the pythagorean theorem of pythagoras and calculating unknown sides with the help of this theorem

[lo 4.2.1, 4.8, 4.9, 4.10]

  • The following could be done in groups.

Practical exercise: Making you own tangram.

1. Cut out a cardboard square (10 cm x 10 cm).

2. Draw both diagonals, because they form part of the bases of some figures.

3. Divide the square in such a way that the complete figure consists of the following:

3.1 two large equilateral triangles with bases of 10 cm in length;

3.2 two smaller equilateral triangles, each with base 5 cm in length;

3.3 one medium equilateral triangle with adjacent sides 5 cm in length;

3.4 one square with diagonals of 5cm;

3.5 one parallelogram with opposite sides of 5 cm.

  • Make two of these. Cut along all the lines so that you will have two sets of the above shapes.

4. Now trace the largest triangle of your tangram in your workbook as a right-angled triangle.

5. Arrange the seven pieces to form a square and place this on the hypotenuse of the traced triangle.

6. Now arrange the two largest triangles to form a square and place this on one of the sides adja­cent to the right angle of the traced triangle.

7. Arrange the remaining pieces to form a square and place this on the other adjacent side.

Questions & Answers

what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
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
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?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
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 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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