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Grade 9

Quadrilaterals, perspective drawing,transformations

Module 23

Understanding quadrilaterals and their properties in problems


To apply understanding of quadrilaterals and their properties in problems

[LO 3.7, 4.4]

  • All the figures for this section are on a separate problem sheet. Use it together with the questions that follow here.
  • Work in pairs as follows: first study each problem independently until you have solved it or gone as far as you can. Then explain your solution carefully, and step by step, to your partner, until he understands it well enough to write it down. In the following problem it will be your partner’s turn to explain his solution to you for writing down. You should remember to give a reason or explanation for everything you do.

1. Calculate the values of a, b, c , etc. from the information given here and in the sketch, and answer the question.

1.1 The diagram shows a square with one side 3 cm. a = an adjacent side.

b = the diagonal. c = the area of the square.

Why does the diagonal make a 45 ° angle with the side?

1.2 A rhombus is given, with long diagonal = 8 cm and short diagonal = 6 cm. a = side length.

b = area of rhombus..

Why are you allowed to use the Theorem of Pythagoras here?

1.3 The diagram shows a rectangle with a short side = 5 cm and a diagonal = 13cm.

a = the long side. b = area of rectangle.

Why is the other diagonal also 13 cm?

1.4 The figure is a parallelogram with one internal angle = 65°, height = 3 cm and long side = 9 cm.

a = smaller of internal angles. b = larger of internal angles. c = area of parallelogram

Explain why this parallelogram has the same area as a 3 cm by 9 cm rectangle.

2. Calculate the value of x from the information in the sketches.

2.1 An equilateral triangle is given, with side 15 cm and area = 45 cm 2 . x = height of triangle.

Why does this triangle have a 60 ° internal angle?

2.2 The diagram shows a trapezium with longest side 23 cm and the side parallel to

it 15 cm and height = 8 cm.

x = area of trapezium.

Why are the two marked internal angles supplementary?

2.3 The figure is a kite with area 162 cm 2 and a short diagonal of 12 cm. x = long diagonal.

Why do the internal angles of the kite add up to 360 ° ?

2.4 The sketch shows the kite from question 2.3 divided into 3 triangles with equal areas (ignore the dotted line). x = top part of long diagonal.

3. These problems require you to make equations from the information in the sketch, using your knowledge of the characteristics of the figure. Solving the equations gives you the value of x .

3.1 The figure is a rhombus with two angles marked 3 x and x respectively.

Why can’t we call this figure a square?

3.2 In the parallelogram, two opposite angles are marked x + 30° and 2 x – 10° respectively.

Explain why the marked angle is 110 ° .

3.3 The trapezium shows the two marked angles with sizes x – 20° and x + 40° respectively.

Why is this not a parallelogram?

3.4 Given is a rhombus with the short diagonal drawn; one angle made by the diagonal is 50° and one internal angle of the rhombus is marked x .

Shape sheet

Problem sheet


LO 3
Space and Shape (Geometry)The learner will be able to describe and represent cha­racteristics and relationships between two-dimensional shapes and three–dimensional objects in a variety of orientations and positions.
We know this when the learner:
3.2 in contexts that include those that may be used to build awareness of social, cultural and environmental issues, describes the interrelationships of the properties of geometric figures and solids with justification, including:
3.2.2 transformations.
3.3 uses geometry of straight lines and triangles to solve problems and to justify relationships in geometric figures;
3.4 draws and/or constructs geometric figures and makes models of solids in order to investigate and compare their properties and model situations in the environment;
3.6 recognises and describes geometric solids in terms of perspective, including simple perspective drawing;
3.7 uses various representational systems to describe position and movement between positions, including:ordered grids
LO 4
MeasurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.
We know this when the learner:
4.4 uses the theorem of Pythagoras to solve problems involving missing lengths in known geometric figures and solids.

Questions & Answers

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 ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
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.
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
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
what is the k.e before it land
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
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali 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 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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