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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

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
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 ?
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?
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
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
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what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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