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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

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..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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.
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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