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2. Try doing the following:

  • Draw any acute-angled Δ size 12{Δ} {} PQR .
  • Construct PS size 12{ ortho } {} QR .
  • What is the meaning of PS size 12{ ortho } {} QR ?

Activity 4

Constructing inscribed and circumscribed circles

[lo 3.4, 3.5, 4.7]

1. Constructing a circumscribed circle:

  • Draw any acute-angled triangle.
  • Bisect all three angles. You will notice that the tree bisecting lines meet in a single point.
  • Try to locate the distance where you could position your compass to draw a circle within or around the triangle.
  • Explain what the distance was at which you were able to draw an accurate circle around the triangle.
  • What is this distance called?
  • What type of circle could you draw?

1.7 Conclusion: A . circle can be constructed by

bisecting the of a triangle.

2. Constructing an inscribed circle:

  • Draw any acute-angled triangle.
  • Bisect all three angles. You will notice that the tree bisecting lines meet in a single point.
  • Try to locate the distance where you could position your compass to draw a circle within or around the triangle.
  • Explain what the distance was at which you were able to draw an accurate circle inside the triangle.
  • What is this distance called?
  • What type of circle could you draw?

2.7 Conclusion: A circle can be constructed by

bisecting the of a triangle.

Activity 5

Constructing a line parallel (ll) to a requested line with the help of a pair of compasses

[lo 3.4, 3.5, 4.7]

1. Required: construct FA ll QR , so that AR = 30 mm.

1.1 Draw an imaginary line (dotted line) FA where the parallel line is required to be.

1.2 Mark A on PR so that AR = 30 mm.

1.3 Position the point of your compasses on R and draw an arc (any size) as indicated.

1.4 Maintaining the setting of your pair of compasses (same size), place the point on A and draw an arc like the previous one.

1.5 Measure the distance, marking it with crosses (x) as indicated.

1.6 Place the compass point on the circle (o) as indicated. This line will intersect the arc and should be on the imaginary line.

1.7 Connect A with the intersecting point of the last drawn line.

1.8 Mark F on PQ. FA will be parallel to QR .

1.9 What does it mean when we say that FA ll QR ?

2. Try doing the following by yourself:

  • Construct any obtuse-angled Δ size 12{Δ} {} PQR .
  • Bisect PR and designate the centre F .
  • Draw a line through F parallel to QR .
  • The parallel line PQ must intersect G .

Activity 6

Constructing a parallelogram

[lo 3.4, 3.5, 4.7]

1. You are the owner of a farm in Mpumalanga. You wish to reward one of your farm workers, Michael Mohapi, for his good service of the past 20 years. You present Michael with a stretch of land as a gift. The precondition is that the land must be measured out in the form of a parallelogram according to measurements indicated on a plan.

1.1 The first problem that arises has to do with the fact that Michael does not know what a parallelogram is. Use a sketch to provide Michael with all the characteristics of a parallelogram.

1.2 Also show Michael the mathematical “abbreviation” for a parallelogram, so that he will know what is meant when he sees the relevant "sign".

1.3 Now you have to execute a construction to indicate exactly how the land is to be measured.


LO 3
Space and Form (geometry)The learner is able to describe and represent features of and relationships between two-dimensional forms and three-dimensional objects in a variety of orientations and positions.
We know this when the learner:
3.2 describes and classifies geometric figures and three-dimensional objects in terms of properties in contexts inclusive of those that can be used to promote awareness of social, cultural and environmental issues, including:3.2.1 sides, angles and diagonals and their relationships, focusing on triangles and quadrilaterals (e.g. types of triangles and quadrilaterals);
3.3 uses vocabulary to describe parallel lines that are cut by a transverse, perpendicular or intersection line, as well as triangles, with reference to angular relationships (e.g. vertically opposite, corresponding);3.4 uses a pair of compasses, a ruler and a protractor for accurately constructing geometric figures so that specific properties may be investigated and nets may be designed;3.5 designs and uses nets to make models of geometric three- dimensional objects that have been studied in the preceding grades and up till now;3.7 uses proportion to describe the effect of expansion and reduction on the properties of geometric figures;3.8 draws and interprets sketches of geometric three-dimensional objects from several perspectives, focusing on the retention of properties.
LO 4
MeasuringThe learner is able to use appropriate measuring units, instruments and formulas in a variety of contexts.
We know this when the learner:
4.1 solves more complicated problems involving time, inclusive of the ratio between time, distance and speed;4.2 solves problems involving the following:4.2.1 length;4.2.2 circumference and area of polygons and circles;4.2.3 volume and exterior area of rectangular prisms and cylinders;
4.3 solves problems using a variety of strategies, including:4.3.1 estimation;4.3.2 calculation to at least two decimal points;4.3.3 use and converting between appropriate S.I. units;
4.5 calculates the following with the use of appropriate formulas:4.5.1 circumference of polygons and circles;4.5.2 area of triangles, right angles and polygons by means of splitting up to triangles and right angles;4.5.3 volume of prisms with triangular and rectangular bases and cylinders;
4.7 estimates, compares, measures and draws triangles accurately to within one degree.



The memorandum of this learning unit is done by the learners and /or determined by the teacher for corrections.


1. Both pairs opposite sides are equal.

2. Both pairs opposite sides are parallel.

3. Both pairs opposite angles are equal.

4. Diagonals bisect each other.

5. One pair opposite sides – equal and parallel.

Questions & Answers

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.
what is biological synthesis of nanoparticles
Sanket 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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