<< Chapter < Page Chapter >> Page >

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

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
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Mathematics grade 8' conversation and receive update notifications?

Ask