<< Chapter < Page Chapter >> Page >


Grade 8

Ratio and proportion



Module 17

Constructing different angles and triangles

Activity 1

Constructing different angles and triangles

[lo 3.4, 3.5, 4.7]

1. Drawing an angle:Requirements: pencil, ruler, protractor.

1.1 Always begin by drawing a base line.

1.2 Make a mark, e.g. on the left, and position the protractor on the mark.

1.3 Read your protractor from 0°.

1.4 In the case of an angle that is larger than 180°, the relevant angle size must be deducted from 360° before it is drawn. The angle around the outside (the reflex angle) is the angle that you will have to draw.

E.g. 320°: (360° – 320° = 40°). Draw a 40°angle. The reflex angle now represents the 320°.

2. Construct the following angles and name each one:

  • A B ˆ size 12{ { hat {B}}} {} C = 75°

Type of angle:

2.2 C D ˆ size 12{ { hat {D}}} {} E = 135°

Type of angle:

2.3 F G ˆ size 12{ { hat {G}}} {} H = 215°

Type of angle:

3. Constructing a triangle:

Requirements: pencil, ruler, protractor and pair of compasses.

  • Always begin by making a rough sketch.
  • Then use one of the sides of which the length is provided as a base.
  • E.g. construct Δ size 12{Δ} {} ABC with BC = 40 mm, B ˆ size 12{ { hat {B}}} {} = 70° and C ˆ size 12{ { hat {C}}} {} = 50°.

Rough sketch:

  • To measure a lateral length accurately, you must measure the length on you ruler with the help of a pair of compasses. Then the compass point must be positioned on B and the position of C must be indicated with a pencil mark.
  • Construction:

4. Construct each of the following triangles:

4.2 Δ size 12{Δ} {} PQR with QR = 58 mm, P Q ˆ size 12{ { hat {Q}}} {} R = 62° and Q P ˆ size 12{ { hat {P}}} {} R = 69°.


  1. PQ = mm
  2. R ˆ size 12{ { hat {R}}} {} =

4.2 Isosceles Δ size 12{Δ} {} ABC with BC = 42 mm, AB = AC and B ˆ size 12{ { hat {B}}} {} = 63°.


a) PQ = mm

Activity 2

Bisecting any given line or angle

[lo 3.4, 3.5, 4.7]

  1. Bisecting a given line AB :
  • Measuring line segment AB (e.g. 40 mm).
  • Using a pair of compasses, measure slightly more than half of the line(i.e. ± 22-25 mm).
  • Position the point of the pair of compasses on A and make a pencil stroke below and above the line.
  • Position the point of the compasses on B and draw another pencil stroke above and below the line.
  • Connect the intersections of the pencil strokes.
  • Name the point on line AB , P. P is the centre of line AB .

2. Now try the following:

  • Draw line segment PQ = 70 mm.
  • Bisecting line segment PQ , as in nr. 1 explained.

3. Bisect π ABC :

  • Place the point of the pair of compasses on B .
  • Draw an arc of any size as indicated.
  • Position the point of the compass on the point where the two lines intersect and draw pencil lines inside the angle.
  • Position the point of the compass on the other point of intersection and draw a line inside the angle, so that the two lines intersect.
  • Connect B ˆ size 12{ { hat {B}}} {} (angle B ) with the point where your pencil lines intersect.
  • B ˆ size 12{ { hat {B}}} {} 1 will have the same size as B ˆ size 12{ { hat {B}}} {} 2 . Measure both angles. Are they equal?

4. Try the following:

  • Draw D E ˆ size 12{ { hat {E}}} {} F = 125°.
  • Bisect D E ˆ size 12{ { hat {E}}} {} F .

Activity 3

To construct a line perpendicular from a given point to another line

[lo 3.4, 3.5, 4.7]

1. Construct AD size 12{ ortho } {} BC .

  • Place your compass point on A (you want to draw a perpendicular line on BC from A.)
  • Make an arc on BC .
  • Place the point of your compasses on the one point of intersection between the arc and BC. Draw a line below BC. Place the point of your compasses on the other point of intersection between the arc and BC and draw another line below BC , so that the two lines intersect.
  • Connect A with the intersection of the two drawn lines.
  • Mark the point of intersection D .
  • AD will be perpendicular to BC . ( AD size 12{ ortho } {} BC .)

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
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?