How to use this book


Welcome to the Oxford Successful Mathematics series Grade 9. This series is based on the National Curriculum Statement: Curriculum and Assessment Policy issued by the Department of Basic Education.


On the first page of each chapter, you will find a mind map that shows you what topics will be covered. At the end of each chapter, you will find the following: • a chapter summary that will help you to quickly revise the chapter’s work; and


• a consolidation exercise consisting of revision questions to test how much you have learnt in the chapter.


You will see the following throughout the book: UNIT 4 Congruency and similarity


In this unit you will: • identify congruent triangles • prove that two triangles are congruent • identify similar triangles • prove that two triangles are similar.


In Geometry, polygons are congruent if they are identical, that is, all their sides and corresponding angles are equal. If you cut out congruent polygons with your scissors, you would be able to fit them exactly over one another.


In Maths the accepted abbreviation for congruent is ≡. It looks like a triple equals sign.


Congruent triangles


You now need to take another look at some of the triangles you have constructed in the previous units of this chapter. Table 1 below summarises which examples are congruent and what you can discover from them.


Table 1 Conditions for a congruent triangle Unit and Exercise number


Unit 1, Exercise 2, numbers 1 and 2


Unit 1, Exercise 3, number 1


Unit 3, Exercise 2, numbers 1 and 2


Unit 3, Exercise 3, number 1


In this unit you will: This breaks down exactly what you will learn in the unit.


New words


congruent: identical in shape and size.


corresponding: angles in the same relative position as one another.


New words: Key words to learn and remember in this subject.


What was measured for the construction


3 sides of the triangle


2 angles and the side between them


A right angle, the


hypotenuse and one other side


2 sides and the angle between them


Abbreviation Side, side, side (SSS) Angle, side, angle (ASA)


Right angle, hypotenuse, side (RHS)


Side, angle, side (SAS) Unit 4: Congruency and similarity 177


• the bases are parallel to one another • the side of the cylinder is one curved surface • the curved surface forms a rectangle when flattened • the length of the rectangle is equal to the circumference of the base • the radius of a cylinder is the distance from the centre of the base to its circumference.


Building cylinders


A cylinder is a 3D object with two circular bases and one curved surface. The curved surface is a single rectangle. When you draw the net of a cylinder, you need to be able to work out the circumference of the circle so that you know how long to draw the width of the rectangle.


r base h


Circumference of a circle C = 2πr where π = 22


__ 7


r = radius of circle


Diagrams and illustrations: These make it easier for you to understand the text.


base Worked example


Build a cylinder with radius 3 cm and height 12 cm. Construct the net on stiff paper.


Solution radius


Draw a circle of radius 3 cm.


C = 2πr C = 2π(3) C = 18,85 cm


Calculate the circumference of the circle. This will give the length of the rectangle.


18,85 cm 12 cm


Construct a rectangle below the circle. The rectangle must be 18,85 cm long by 12 cm wide. The height of the cylinder must be 12 cm, so the width of the rectangular side will be 12 cm. The rectangle must touch the edge of the circle but not cut through it.


Unit 3: Spheres and cylinders 385


Narrated worked examples: Before you are asked to attempt any exercise, we give you a narrated example explaining how to tackle the work.


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How to use this book


CHAPTER 14


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