25

Topic 5 Angle properties

b) 75° 3x = 180° [Angles on a straight line = 180°.] \ x = 35° ∠D = 180° 35° 75° [Sum of angles of a triangle = 180°.] \ ∠D = 70° ∠D = 70°, ∠E = 35° and ∠F = 75° \ DEF is an acute-angled scalene triangle. c) x 2x 60° 3x 120° = 180° [Sum of angles of a triangle = 180°.] \ x = 60° ∠G = 60°, ∠H = 60° and ∠I = 60° \ GHI is an equilateral triangle. d) 2x 3x x 3x 45° = 360° [Sum of angles of a quadrilateral = 360°.] \ x = 45° ∠J = 90°, ∠K = 135°, ∠L = 45° and ∠M = 90° \ JK || ML [Co-interior angles are supplementary.] \ JKLM is a trapezium. e) x 110° x x __ 2 = 360° [Sum of angles of a quadrilateral = 360°.] \ x = 100° ∠N = 100°, ∠O = 110°, ∠P = 100° and ∠Q = 50° \ NOPQ is a kite. f) ∠U 66° = 180° [Angles on a straight line = 180°.] \ ∠U = 114° x 16° 2x 14° 2x 34° 114° = 360° [Sum of angles of a quadrilateral = 360°.] \ x = 50° ∠R = 66°, ∠S = 114°, ∠T = 66° and ∠U = 114° \ RSTU is a parallelogram.3 a) ∠DCA = ∠DAC [Isosceles ACD; CD = AD.] 124° 2(90° 2x) = 180° [Sum of angles of a triangle = 180°.] \ x = 31° b) i) ∠DCA = 28° ii) ∠DAC = 28° iii) ∠BAC = 31° iv) ∠BCA = 59° c) i) ACD is an obtuse-angled isosceles triangle. ii) ABC is a right-angled scalene triangle.

26

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6 Geometrical constructions

Unit Topic General objective

Specific objective Activity/Exercise

SB page number

2.2 Geometry 2.2.1 Geometrical constructions

2.2.1.1 Construct geometrical shapes and understand the properties of triangles and quadrilaterals.

2.2.1.1.1 Construct triangles from given data.

2.2.1.1.2 Identify congruent triangles and their corresponding measures.

2.2.1.1.3 Identify similar triangles and their properties.

2.2.1.1.4 Construct quadrilaterals from given data.

2.2.1.1.5 Identify congruent quadrilaterals and their corresponding measures.

Exercise 1Activity 1Exercise 2Activity 2Revision

Activity 3Exercise 3Activity 4Revision

Activity 4Exercise 4Revision

Exercise 5Exercise 6Revision

Exercise 7Activity 5Revision

5151525259

54545559

555559

575759

585859

RationaleStudying geometry is important because it requires students to reason and to think about how they •reason. In this topic, students explore the properties of triangles and quadrilaterals by constructing and comparing them.They will also learn about the concepts of congruency and similarity. Approach the geometrical proofs step •by step so that students develop logical and disciplined thinking and reasoning.

Additional informationFocus on the congruency of triangles. Students often struggle with the order in which to write the letters •of the triangles. Explain that the order of the letters of the first triangle is not important. In this topic, we usually write the letters of the first triangle alphabetically. However, the letters in the second triangle must match the letters in the first triangle.Explain that if two triangles are not congruent, the order in which we write the letters is not important. •When two triangles are not congruent, we use the symbol “ ” to show the incongruency.Some students may need extra practice, so give them as many additional examples as you feel are necessary.•

Answers

Oral activity Discuss the construction of an Egyptian pyramid (SB p. 50)

1 One example is “building”.2 a) Both types of constructions use the same basic 2D shapes and both types of constructions require

accurate measurements.

27

Topic 6 Geometrical constructions

b) The students’ constructions will be 2D, while the pyramids are 3D; their constructions will be on paper, while the Egyptians constructed real-life objects, and their constructions will be on a different scale to those of the Egyptians.

3 a) The outline of the pyramid in the background b) The face of a cuboid in the stone or marble slabs in the foreground4 North Africa

Exercise 1 Construct triangles given all three sides (SB p. 51)

1 Students construct a triangle with sides of 9.5 cm, 8 cm and 7.5 cm.2 Students construct a triangle with sides of 10 cm, 8 cm and 6 cm.3 Students construct a triangle of which two sides are 70 mm and the third side is 45 mm.4 Students construct a triangle of which all three sides are 55 mm.5 Students construct a triangle of which two sides are 5 cm each and the third side is 60 mm.6 Students construct a triangle of which all three sides are 4.5 cm.7 Students construct a triangle with sides of 6 cm, 4 cm and 60 mm.8 Students construct a triangle with sides of 8.5 cm, 90 mm and 56 mm.

Activity 1 Discuss constructions of triangles given all three sides (SB p. 51)

1 Let students discuss the statement.2 Acute-angled scalene triangle; right-angled scalene triangle; acute-angled isosceles triangle; equilateral

triangle

Exercise 2 Construct triangles given two sides and the angle between them (SB p. 52)

1 Students construct a triangle of which two sides are 85 mm, and the angle between these sides is 60°.2 Students construct a triangle of which two sides are 6.7 cm and 53 mm, and the angle between these

sides is 110°.3 Students construct a triangle of which two sides are 6 cm and 4 cm, and the angle between these

sides is 90°.4 Students construct a triangle of which two sides are 70 mm, and the angle between these sides is 110°.5 Students construct a triangle of which two sides are 8 cm and 70 mm, and the angle between these

sides is 130°6 Students construct a triangle of which two sides are 5.3 cm, and the angle between these sides is 60°.7 Students construct a triangle of which two sides are 58 mm and 4.2 cm, and the angle between these

sides is 30°.8 Students construct a triangle of which two sides are 4.9 cm, and the angle between these sides is 90°.

Activity 2 Discuss constructions of triangles given two sides and the angle between them (SB p. 52)

1 Equilateral triangle2 Obtuse-angled scalene triangle3 Right-angled scalene triangle4 Obtuse-angled isosceles triangle5 Obtuse-angled scalene triangle6 Equilateral triangle7 Acute-angled scalene triangle8 Right-angled isosceles triangle

28

Topic 6 Geometrical constructions

Exercise 3 Identify congruent triangles (SB p. 54)

1 and 2 a) ABC DFE (AAS) b) The triangles are not congruent. c) XYZ BAC (RHS) d) PQR SUT (AAS) e) The triangles are not congruent. f) JKL NMO (SSS) or JKL NOM (SSS)

Activity 3 Discuss the four conditions of congruency for triangles (SB p. 54)

1 Students discuss the four conditions of congruency for triangles.2 Students must realise that the corresponding letters of the triangles must match when they write a

congruency statement.

Activity 4 Discuss congruency and similarity (SB p. 55)

1 Pako is correct. Congruent figures always have the same shape, but similar figures do not necessarily have the same size.

2 Neo is correct. If two angles of a triangle are respectively equal to two angles of another triangle and have the values x and y respectively, then the unknown angles will both have the values of (180° x y). They will, therefore, also be equal.

Exercise 4 Identify similar triangles (SB p. 55)

1, 2 and 3 a) ∠P = 110°; ∠T = ∠U = 35° \ PQR STU (AAA) b) ∠X = 65°; ∠A = 35° \ The triangles are not similar, because their angle sizes do not correspond. c) ∠D = 60°; ∠Q = 65° \ DEF PRQ (AAA)

Exercise 5 Construct rectangles, squares, parallelograms and rhombuses (SB p. 57)

1 Students construct a rectangle with sides of 7.5 cm and 62 mm.2 Students construct a rectangle with sides of 37 mm and 5.5 cm.3 Students construct a square with sides of 8.1 cm.4 Students construct a square with sides of 46 mm.5 Students construct a parallelogram with sides of 8 cm and 6 cm, and an angle between them of 60°.6 Students construct a parallelogram with sides of 9 cm and 5 cm, and an angle between them of 135°.7 Students construct a parallelogram with sides of 4 cm and 62 mm, and an angle between them of 80°.8 Students construct a rhombus with sides of 68 mm, and an angle of 25°.9 Students construct a rhombus with sides of 7.5 cm, and an angle of 130°.10 Students construct a rhombus with sides of 69 mm, and an angle of 75°.

Exercise 6 Construct a kite and a trapezium (SB p. 57)

1 Students construct a kite as shown in the diagram.2 Students construct an isosceles trapezium that consists of three equilateral triangles, each with a side

length of 5.5 cm.3 Students construct a kite with sides of 4.5 cm and 6.5 cm.4 Students construct a trapezium with the two parallel sides 7 cm and 9 cm, and a distance between

them of 5 cm.

29

Topic 6 Geometrical constructions

Exercise 7 Work with congruent quadrilaterals (SB p. 58)

1 a) SSS b) AAS c) Yes. The corresponding angles in both quadrilaterals are equal and the corresponding sides

are also equal.2 a) ∠E = 95°; ∠Y = 80° b) Although the quadrilaterals have the same angle sizes, the equal angles are not in the corresponding

positions. In addition, no sides are given, so we cannot say whether they are congruent or not.3 LM = 6 cm; MN = 10 cm; NO = JK = 6.5 cm; LO = 7.5 cm; ∠K = 112.6°; ∠N = ∠J = 67.4°

Activity 5 Discuss congruency in quadrilaterals (SB p. 58)

1 Yes. Their sides are all x cm and their angles are all 90°.2 No. Their sides are all x cm, but their angles do not necessarily correspond.3 Yes. They have two pairs of opposite sides of x cm and y cm respectively, and their angles are all 90°.4 No. They have two pairs of opposite sides of x cm and y cm respectively, but their angles do not necessarily

correspond.5 No. They have two pairs of adjacent sides of x cm and y cm respectively, but their angles do not necessarily

correspond.

Revision (SB p. 59)

1 Students construct two isosceles triangles. In one triangle, there are two sides of 4.5 cm and one side of 5 cm. In the other triangle, there are two sides of 5 cm and one side of 4.5 cm.

2 a) ABC YZX (AAS) b) The triangles are not congruent. c) LMN EDF (SSS)3 Students construct a parallelogram with sides of 10 cm and 7.5 cm, and an angle between them of 145°.4 a) AD = BC = ST = VU = 7 m; BA = CD = SV = TU = 18 m; ∠C = ∠A = ∠V = ∠T = 117°; ∠B = ∠D = ∠S = ∠U = 63° b) quadrilateral BCDA UVST (or STUV)5 a) No b) Students’ own sketches. The two parallel sides of the trapezium are the 5-cm side and the side opposite

it. However, the distance between the two parallel sides can vary.6 a) Isosceles trapeziums b) DE = DG = EF = QR = PS = PQ = 3 cm; RS = FG = 6 cm; ∠R = ∠F = ∠G = ∠S = 59°;

∠D = ∠E = ∠P = ∠Q = 121°

30

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7 Polygons

Unit Topic General objective

Specific objective Activity/Exercise

SB page number

2.2 Geometry 2.2.3 Polygons 2.2.3.1 Demonstrate skills of constructing polygons.

2.2.3.1.1 Construct regular polygons from given data.

2.2.3.1.2 Use reflection, translation and rotation to draw congruent polygons on a coordinate grid.

2.2.3.1.3 Use enlargement and reduction to draw similar polygons on a coordinate grid.

Activity 2Exercise 1Exercise 2Revision

Activity 3Exercise 3Activity 4Exercise 4Activity 5Exercise 5Revision

Exercise 6Revision

62626369

64656566676769

6869

RationaleThis topic builds on students’ existing knowledge of polygons. In this topic, they will construct regular •polygons from given information. They will also use transformations to draw congruent and similar polygons on a Cartesian plane.It is important that students understand this work on polygons. They need this knowledge to be able to •work with perimeter and area of 2D shapes, and total surface area and volume of 3D objects in later topics.

Additional informationStudents need to know the terminology and definitions that relate to polygons, such as triangle, •quadrilateral, pentagon, hexagon and octagon. They must also know that a vertex is a corner. Ensure that they can define a polygon and that they understand the difference between a regular and an irregular polygon. Ensure that they also understand the difference between a convex polygon and a concave polygon.Explain that a regular polygon is a polygon of which all the sides are equal • and all the angles are equal. Test their understanding of this definition by drawing a rhombus on the board. Draw the rhombus so that it looks like opposite angles are not equal, but show that the four sides are equal using markers. Conduct a class discussion about whether the rhombus is a regular polygon or not. Note, a rhombus is not a regular polygon, because its angles are not all equal.Students usually enjoy working with transformations but have difficulty remembering the terminology. •Provide enough practice with rigid transformations translations, reflections and rotations before you begin the section on enlargements and reductions. Remind students that a translation is a slide, a reflection is a mirror image and a rotation is a turn.The table on page 69 of the Student’s Book summarises useful algebraic rules for describing transformations •on a Cartesian plane. Help students who are not confident with abstract thinking to understand these rules. Give them extra examples to demonstrate how each rule works.

31

Topic 7 Polygons

Answers

Oral activity Compare polygons (SB p. 60)

1 Pentagon2 Hexagon3 a) Both are regular polygons because their sides are all the same length and their angles are all equal. b) Their number of sides is different.

Activity 1 Revise names and properties of polygons (SB p. 61)

1 a) Triangle b) Quadrilateral c) Pentagon d) Hexagon e) Heptagon f) Octagon g) Nonagon h) Decagon i) Dodecagon j) Icosagon2 n angles3 a) A convex polygon is a polygon of which none of the internal angles is a reflex angle. A concave

polygon is a polygon of which at least one of the internal angles is a reflex angle. b) Students draw an example of a convex polygon. c) Students draw an example of a concave polygon.4 deca-: ten; dodeca-: twelve; hepta-: seven; hexa-: six; icosa-: twenty; octa-: eight; penta-: five; poly-: many;

tri-: three

Activity 2 Discuss regular triangles and quadrilaterals (SB p. 62)

1 Equilateral triangle2 60°3 The length of one side4 Square5 90°6 The length of one side

Exercise 1 Construct regular triangles and quadrilaterals (SB p. 62)

1 a) Students construct an equilateral triangle with sides of 6 cm. b) Students construct an equilateral triangle with sides of 85 mm. c) Students construct a square with sides of 6 cm. d) Students construct a square with sides of 85 mm.2 b) Yes c) Yes

Extension Construct regular quadrilaterals outside and inside a circle (SB p. 62)

1 Students construct a regular quadrilateral with sides of 7 cm.2 Students construct a circle inside the regular quadrilateral.3 Students construct a regular quadrilateral inside the circle.4 a) 99 mm b) 70 mm c) 49.5 mm d) 70 mm5 The answer to Question 4a) is double the answer to Question 4c).

Exercise 2 Construct regular polygons that have more than four sides (SB p. 63)

1 Students construct a regular pentagon with sides of: a) 6 cm b) 75 mm2 Students construct a regular hexagon with sides of: a) 6 cm b) 75 mm3 Students construct a regular octagon with sides of: a) 6 cm b) 75 mm

32

Topic 7 Polygons

Extension Construct a regular hexagon inside a circle (SB p. 63)

The students need to find a way to construct a regular hexagon inside a circle using only a pair of compasses, a ruler and a sharp pencil. They may struggle with the fact that they cannot use the traditional methods. They will find the solution by experimenting, rather than reasoning.

The method entails first drawing a circle, then marking off one vertex on the circumference of the circle. From there, students need to experiment using the pair of compasses. Ensure that your students have a comfortable setting on their pair of compasses and that they do not change this setting. Check that the pairs of compasses are not too loose. If they are, use a screwdriver to tighten them.

Guide them up to this point if they do not know how to start. Then, leave them to find the solution on their own. The diagram alongside illustrates the solution.

Activity 3 Discuss a translation on a Cartesian plane (SB p. 64)

1 Right-angled scalene triangle2 Yes3 a) Yes b) The triangles have the same shape and the same size.4 a) Translate A'B'C' 4 units to the right and 2 units downwards. b) (x; y) (x 4; y 2)5 a) Translate ABC 1 unit to the left and 3 units downwards. b) (x; y) (x 1; y 3)6 a) Translate A'B'C' 3 units downwards. b) (x; y) (x; y 3)

Exercise 3 Use translations to draw congruent polygons (SB p. 65)

1 Parallelogram2

54321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5

0AD

Q U

A'D'

Q' U'

3 54321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5

0AD

Q U

A''D''

Q'' U''

(x; y) (x 4; y 4)4 (x 1; y 5)

33

Topic 7 Polygons

Activity 4 Discuss the reflection of a point in the y-axis, the x-axis and the line y = x (SB p. 65)

1 Students should agree with the reasoning.2 a) (x; y) b) (x; y) (x; y)3 a) ( y; x) b) (x; y) ( y; x)

Exercise 4 Use reflections to draw congruent polygons (SB p. 66)

1 a) 654321

–1–1 1 2 3 4 5 6

y

x–2–3–4–5–6

–2–3–4–5–6

0

y = xPP'QQ'

RR'

b) 654321

–1–1 1 2 3 4 5 6

y

x–2–3–4–5–6

–2–3–4–5–6

0

y = xP

P'

Q

Q'

R

R'

c) 654321

–1–1 1 2 3 4 5 6

y

x–2–3–4–5–6

–2–3–4–5–6

0

y = xP

P'

Q

Q'R

R'

2 a) Kite b) PQ = P'Q and PR = P'R

Activity 5 Discuss the rotation of a point around the origin (SB p. 67)

1 a) Students discuss how to rotate point P around the origin through 90°. b) (x; y) (y; x)2 a) Students discuss how to rotate point P around the origin through 180°. b) (x; y) (x; y) c) No d) A clockwise rotation around the origin through 180° has the same effect as an anticlockwise rotation

around the origin through 180°.3 a) Students discuss how to rotate point P around the origin through 270°. b) (x; y) ( y; x) c) The two rotations have the same effect.4 Rotate some points of the figure around a point, then join these points to form the image.

34

Topic 7 Polygons

Exercise 5 Use rotations to draw congruent polygons (SB p. 67)

1 a) 54321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5

0

PP'

Q'

R'Q

R

b) 54321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5

0

P

P'

Q'

R'

Q

R

c) 54321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5

0

P

P'Q'

R'

Q

R

2 a) P'(1; 1), Q'(4; 2) and R'(3; 3) b) P'(1; 1), Q'(2; 4) and R'(3; 3) c) P'(1; 1), Q'(4; 2) and R'(3; 3)3 a) P'(1; 1), Q'(4; 2) and R'(3; 3) b) P'(1; 1), Q'(2; 4) and R'(3; 3) c) P'(1; 1), Q'(4; 2) and R'(3; 3)4 c) Irregular dodecagon d) 4

Exercise 6 Use enlargements and reductions to draw similar polygons (SB p. 68)

1 Arrowhead2 L'(9; 9), M'(0; 13 1 __ 2 ), N'(9; 9) and O'(0; 0)

3 L'(1; 1), M'(0; 1 1 __ 2 ), N'(1; 1) and O'(0; 0)

Revision (SB p. 69)

1 Students construct a regular hexagon with sides of 8 cm.2 a) K'(1; 2), L'(1; 2) and M'(4; 0) b) 180° c) K'(4; 1), L'(4; 5) and M'(1; 3) d) K'(3; 6), L'(3; 6) and M'(12; 0) e) K'( 1 __ 2 ; 1), L'( 1 __ 2 ; 1) and M'(2; 0)3 2; 180°4 a) (x; y) (x; y) b) (x; y) (x m; y n)

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8 Coordinate geometry

Unit Topic General objective

Specific objective Activity/Exercise

SB page number

2.2 Geometry 2.2.4 Coordinate geometry

2.2.4.1 Gain knowledge on linear and quadratic relationships.

2.2.4.1.1 Draw graphs of the form y = mx c to represent linear relationships.

2.2.4.1.2 Use a spreadsheet to draw graphs of the form y = mx c.

2.2.4.1.3 Find the equation of a straight line of the form y = mx c.

2.2.4.1.4 Draw graphs of the form y = ax2 bx c to represent quadratic relationships.

Activity 1Exercise 1ExtensionActivity 2Case studyRevision

Exercise 2

Activity 3Exercise 3Revision

Activity 4Exercise 4Case studyRevision

737474757581

76

787881

798080 81

RationaleIn this topic, students will draw graphs of straight lines and parabolas for the first time. This work builds on their knowledge of algebraic equations because they will relate each equation to its graph. They will also gain extra experience of spreadsheets when they use spreadsheets to draw straight-line graphs.

Additional informationWhen students draw a graph of an algebraic equation, some may struggle to see how a graph can represent •an equation, because this concept is new to them. They may associate graphs with data handling and not with algebra. Therefore, take your time as you work through this topic.When students work with spreadsheets, you may find that some students are more computer literate than •others. Pair your students carefully, keeping in mind which students are likely to cope well with this work. If your computer resources are limited, divide the class into small groups instead of pairs. Consider asking the Computer Awareness teacher for advice if and when required. They could even give your class a brief introduction to Microsoft Excel® before they begin this practical work.

Answers

Oral activity Discuss the Cartesian plane (SB p. 72)

1 Quadrants2 The axes go on forever.3 a) Write the two variables inside brackets separated by a semi-colon, for example (x; y). b) Write the x-value first followed by the y-value.4 a) Origin b) (0; 0)5 a) René Descartes b) 17th century (15961650)

36

Topic 8 Coordinate geometry

Activity 1 Discuss a graph of the form y = mx c (SB p. 73)

1 a) True b) m = 1; c = 22 c is the y-value of the point where the graph cuts the y-axis.

Exercise 1 Draw graphs of the form y = mx c (SB p. 74)

1 a) Graph of the equation y = x 2 b) Graph of the equation y = 3x

54321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5

0

y = x – 2

56789

4321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5–6–7–8–9

0

y = 3x

c) Graph of the equation y = 3x 1

56789

4321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5–6–7–8–9

–10

0

y = 3x – 1

d) Graph of the equation y = x 2

54321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5

0

y = −x + 2

e) Graph of the equation y = 2x 4 f) Graph of the equation y = 3x 6

56789

10

4321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5–6–7

0

y = −2x + 4

56789

101112

4321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5–6

0

y = −3x + 6

37

Topic 8 Coordinate geometry

2 Students discuss the influence of m and c on the graphs that they drew in Question 1.3 a) Graph of the equations b) Graph of the equations c) Graph of the equations y = 2x 3 and y = 2x 1 y = 3x 3 and y = 3x 2 y = x 4 and y = x 5

56789

10

4321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5–6–7–8–9

–10

0

y =

2x +

3y

= 2x

− 1

56789

101112

4321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5–6–7–8–9

–10–11–12

0

y = −3x − 3

y = −3x + 2

567

4321

–1–1 1 2 3 4 5 6 7

y

x–2–3–4–5–6–7

–2–3–4–5–6–7

0

y = x

+ 4

y = x

– 5

d) Graph of the equations e) Graph of the equations f) Graph of the equations y = 2x 2 and y = 1 __ 2 x 2 y = 1 __ 4 x 1 and y = 4x 4 y = 3x 6 and y = 1 __ 3 x 1

56789

4321

–1–1 1 2 3 4 5

y

x–2–3–4–5

–2–3–4–5–6–7–8–9

0

y =

2x +

2

y = − x − 21

2

56789

1011121314151617

4321

–1–1 1 2 3 4 5 6

y

x–2–3–4–5–6

–2–3–4–5–6–7–8–9

–10–11–12

0

14y = x + 1

y = –4x + 4

567

4321

–1–1 1 2 3 4 5 6

y

x–2–3–4–5–6

–2–3–4–5–6–7

0

y = –3x + 6

y = x + 113

38

Topic 8 Coordinate geometry

Extension Draw graphs of the form y = c and x = c (SB p. 74)

1 a) i) No ii) The value of y does not depend on the value of x. b) Students’ own answers. From the “Note” on page 74 of the Student’s Book, they should see that the

graph is a straight line. c)

4321

–1–1 1 2 3 4 5

y

x–2–3–4–5 0

y = 2

d) x-axis2 a)

4321

–1–1 1

y

x–2–3–4–5–6

–2–3–4

0

x =

– 4

b) y-axis

Activity 2 Discuss parallel and perpendicular straight-line graphs (SB p. 75)

1 The pairs of graphs are parallel or they have the same gradient, or slope.2 The pairs of graphs are perpendicular.3 parallel4 perpendicularThis conclusion is not easy for students to reach by themselves, so assist them in drawing this conclusion if necessary.

Case study Adopt a family (SB p. 75)

1 a) Yes b) Students’ own reasons c) y = x d) Graph of the equation y = x

108642

2 4 6 8 10

y

x0

y = x

2 a) Yes b) Students’ own reasons c) y = 2x d) Graph of the equation y = 2x

101214161820

8642

2 4 6 8 10

y

x0

y =

2x