geometry workbook

thomaswhitham.pbworks .com

Year 8

Geometry Workbook Mathematics

S J Cooper

Thomas Whitham Sixth Form

Geometry (1) Constructions Name……………………………..

Do the following constructions within the spaces provided [practice first]

1. Perpendicular bisector of AB. 2. Bisector of angle ABC

3. Perpendicular bisector of PQ. 4. Bisector of angle LMN.

5. Bisector of angle EDF. 6. The perpendicular from P to AB.

7. The perpendicular from X to JK. 8. Perpendicular bisector of JK.

A B

A B

C

P

Q

L M

N

D F

E

A B

P

J

K

X J

K

Geometry (2) Constructions Name……………………………..

Do the following constructions within the spaces provided [practice first]

9. Angle 60. Label Point R. 10. Angle ABC=90. Label point C

11. Angle XYZ = 120. Label point Z. 12. Angle QPR = 45. Label point R.

13. Angle MLN = 30. Label point N. 14. Angle ABC = 15. Label point C.

15. Angle DEF = 75 Label point F.

16. Angle STU = 150. Label point S.

P Q A B

P Q

L M A B

X Y

D E T U

Geometry (3) Construction of triangles

Remember do not remove any construction lines or arcs.

1. Draw a triangle ABC whose sides are AB = 7 cm , AC = 5 cm and BC = 4 cm.

Measure and write down the size of angle A.

2. Draw a triangle LMN whose sides are LM = 9 cm , MN = 4 cm and LN = 7 cm.

Measure and write down the size of angle N.

3. Draw a triangle PQR whose sides are PQ = 4 cm , PR = 4 cm and QR = 6 cm.

Measure and write down the size of angle Q.

4. Draw a triangle DEF whose sides are DE = 8 cm , EF = 5 cm and DF = 7 cm.

Measure and write down the size of angle D.

5. Draw a triangle ABC whose sides are AB = 5.4 cm , AC = 3.7 cm and BC = 6.3 cm.

Measure and write down the size of angle C.

6. Draw a triangle XYZ whose sides are XY = 7.2 cm , XZ = 6.2 cm and YZ = 9.4 cm.

Measure and write down the size of angle Z.

7. Draw a triangle LMN whose sides are LM = 4.8 cm , MN = 5.5 cm and LN = 11 cm.

Measure and write down the size of angle N.

8. With the aid of compasses, protractor, rulers, etc...

Draw accurately the following triangles and find the lengths required.

(a) (b) (c)

Angle E = ? Angle P = ? Angle M = ?

3 cm

4 cm

E

6.2 cm

2 cm

7.2 cm 10.4 cm 4 cm

13.4 cm

L

M

N

P

R

Q

9.1 cm


REMEMBER DO NOT REMOVE ANY CONSTRUCTION LINES OR ARCS.

Use Pencil, Ruler, Compass and protractor for questions 1 to 5.

1. Draw a triangle ABC whose side AB = 7 cm and angles BAC = 40 and ABC = 50

Measure and write down the length of side BC.

2. Draw a triangle XYZ , where XY = 4 cm , ZXY = 70 and ZYX = 70 .

Measure and write down the length of ZX.

3. Draw a triangle DEF where DE = 6 cm , EDF = 54 and DEF = 31 .

Measure and write down the length of EF.

4. Draw a triangle PQR where PQ = 4.2 cm , PQR = 35 and QPR = 117 .

Measure and write down the length of side QR.

5. Draw an accurate drawing of the triangle opposite.

Use Pencil, Ruler and Compass only for questions 6 to 10.

6. Draw a triangle PQR where PQ = 3 cm , 90 = RQP and 30 = RPQ .

Measure and write down the length of side QR.

7. Draw a triangle BCD where BC = 8.4 cm , 15 = DCB and 60 = DBC .

Measure and write down the length of side BD.

8. Draw a triangle HIJ where HI = 6.7 cm , 75 = JHI and 60 = JIH .

Measure and write down the length of side IJ.

9. Draw a triangle ABC where AB = 5 cm , 120 = CBA and 30 = CAB .

Measure and write down the length of side AC.

10. Draw a triangle DEF where DE = 7.3 cm , 45 = FDE and 30 = FED .

Measure and write down the length of side DF.

4.6 cm

24 107


REMEMBER DO NOT REMOVE ANY CONSTRUCTION LINES OR ARCS.

Use pencil, ruler, compass and protractor for questions 1 to 5.

1. Draw a triangle LMN where LM = 4 cm , 30 = NML ˆ and MN = 5 cm.

Measure and write down the length of LN.

2. Draw the triangle PQR where PQ = 7 cm, 70 = RPQ ˆ and PR = 4 cm.

Measure and write down the size of RQP .

3. Draw a triangle JKL where JK = 5 cm , 55 = LKJ ˆ and KL = 5.6 cm.

Measure and write down the length of JL.

4. Draw the triangle XYZ where XY = 3.8 cm, 125 = ZXYˆ and XZ = 5.1 cm.

Measure and write down the size of ZYX ˆ .

5. Draw a triangle ABC where AB = 4.3 cm , ABC = 45 and BC = 5.6 cm.

Measure and write down the length of AC.

Use pencil, ruler and compass only for questions 6 to 13.

6. Draw the triangle DEF where DF = 5.3 cm, 60 = EFD and FE = 6.4 cm.

Measure and write down the size of FDE .

7. Draw a triangle STU where ST = 10.7 cm , 45 = UST and SU = 8.5 cm.

Measure and write down the length of TU.

8. Draw the triangle EFG where EF = 9.4 cm, 30 =G FE and FG = 6.7 cm.

Measure and write down the size of EGF ˆ .

9. Draw the triangle PQR where PQ = 8.4 cm, 135 = RQP and QR = 4.7 cm.


10.Draw the triangle EFG where EF = 3.4 cm, 15 =G FE and FG = 5.5 cm.


11. Construct rectangle ABCD where AB = 9 cm and BC = 4 cm.

State the length of the diagonal AC.

12. Construct a rectangle which has dimensions 5.3cm by 11.7cm.

13. Construct rectangle LMNO where LM = 3.9 cm and MN = 6.8 cm.

State the length of the diagonal MO.

14. Construct a rectangle which has dimensions 10.3cm by 5.2cm.

Geometry (6) Error in measurements

In each of the following statements write down the limits between which each of the quantities can

lie.

1. The length of a desk is 57 cm correct to the nearest cm.

2. The height of the desk is given as 29 inches correct to the nearest inch.

3. The length of the classroom is 7400 mm correct to the nearest 100 mm.

4. The weight of John is 82 kg correct to the nearest kg.

5. The weight of Sarah is 120 pounds correct to the nearest 10 pounds.

6. Asif estimates the distance from his house to school is approximately two miles correct to the

nearest mile.

7. The length of a rectangle is 9 cm correct to the nearest cm.

8. The width of the rectangle is given as 40 mm correct to the nearest mm.

9. The distance from Colne to Padiham is given as 19200 m correct to the

nearest 100m.

10. The distance from Burnley to Penzance is 800 miles correct to the

nearest 50 miles.

11. The length of my lounge is 13 feet correct to the nearest foot.

12. The weight of concrete block is 120 kg correct to the nearest 10 kg.

13. The volume of water in a bottle is 2000 cm3 correct to the nearest 100 cm3.

14. Freezing point is given as 0C or 32F correct to the nearest F.

15. A recipe requires 550 grams of sugar correct to the nearest 50 grams.

16. The height of a standard door is 2m correct to the nearest 10 cm.

Geometry (7) Area & Perimeter of rectangles

Work out (i) the area and (ii) the perimeter for each of the rectangles in 1 to 12.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. A photograph 28cm by 23cm is framed

and hung on a wall. The frame is 32cm

by 27cm.Calculate

(a) The area of the photograph

(b) The area of the frame

(c) The area of the frame visible when the

photograph is in place.

7cm

6cm

8 cm

5 cm

7 cm

11 cm

10cm

3cm

8cm

6cm

13cm

4cm

12m

12m

5m

15m

4m

5m

14m

23m

4m

19m

21mm

27mm

28cm

27cm

32cm

23cm

Geometry (8) Area of triangle

Work out the area for each of the following triangles.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. Find the heights of the following triangles.

(a) Area = 21 cm2 (b) Area = 54 cm2 (c) Area = 66 cm2

(d) Area = 240 m2 (e) Area = 27 m2 (f) Area = 750 cm2

25cm 12m

7cm

12cm

8 cm

9 cm

4 cm

7 cm

20cm 6cm

8cm

5m 8mm

15mm

5m

14m

17cm

6m 14m

24m

6cm

h cm

6cm

h cm

11cm

h cm

9m

h m h cm h m

Geometry (9) Area of Irregular shapes

1. Work out (i) the area and (ii) perimeter for each of the following irregular shapes.

(a) (b) (c)

(d) (e) (f)

2. Work out the shaded area for each of the following:

(a) (b) (c)

(d) (e)

22cm

11cm

6cm

9cm 23cm

15cm

8cm

21cm

8cm

3m

3m

3m 18m

9m

7m

17 cm

14 cm

12 cm

23 cm

8 cm

8 cm 14 cm

21 cm 18 cm

25 cm

6 cm

11 cm

19 cm

6 cm

9 cm

6 cm

15 cm

18 cm

31 cm

34 cm

15 cm

8 cm

11 cm 3 cm

17 cm

9 cm

22 cm

22 cm

8 cm

13 cm 7 cm

13 cm

7 cm

4 cm

4 cm

18 cm

12 cm

2 cm

4 cm 4 cm

6 cm 10 cm

3. Work out the area for each of the following (all measurement are in cm):

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

4. Work out the shaded area for each of the following:

(a) (b) (c)

10

12

18

9

7

16

6

5

9

19

3

8

12 8

10

10

6

15

9

8 12

14

5

16

25

13

15

3 4

12

15

7

8

21

9

6

13

5. Find the area of the following irregular shapes.

(a) (b) (c)

(d) (e) (f)

9cm

14cm 15cm

12cm

6cm

10cm

18cm

21cm

36m 24m

54cm

71cm

54cm 13m

21m 27m

Geometry (10) Types of Polygons

1. Name each of the following types of triangles

(a) (b) (c)

(d) (e) (f)

2. Draw a set of axes from –5 to 5 for each of the following problems. Plot the coordinates for each

of the following. Join up the points to form the quadrilateral ABCD. What name is given to each

shape drawn?

(i) A(–2, 2) , B(2, 4) , C(2, 1) , D(–2, –1)

(ii) A(–2, 3) , B(, 4) , C(1, 2) , D(–1, 1)

(iii) A(4, –4) , B(–2, –2) , C(0, 0) , D(3, –1)

(iv) A(2, –3) , B(0, –4) , C(–3, 2) , D(3, –1)

(v) A(–1,–1) , B(–2, 2) , C(2, 3) , D(3, 0)

3. (a) What name best describes a parallelogram with all angles at 90 ?

(b) What name best describes a parallelogram with all sides equal in length?

(c) What name best describes a parallelogram with all sides equal in length and all angles at

90?

4. Name each of the following quadrilaterals

(a) BCDN

(b) JMHI

(c) JMLK

(d) DEFG

(e) DGHN

(f) LKAB

(g) LBNH

A B C

D

G

F

E

I H

K

J

N

M

L

Geometry (11) Solids

1. For each of the tabulated solids below count the number of faces, vertices (corners) and edges.

Enter the numbers in the appropriate place. In the last column work out the value of F + V – E

for each line. State what you notice.

Number of

Faces (F)

Number of

Vertices (V)

Number of

Edges (E)

F + V – E

Cube

Cuboid

Square based pyramid

Tetrahedron

Triangular prism

2. A block of butter is in the shape of a cuboid until someone

cuts away a corner with a knife, as shown. Count up

faces, vertices and edges on the remainder of the butter

shown. Complete the following.

F =……….. V = …………. E = ………….

F + V – E = …………….

3. (a) Using a pencil draw a sketch of a square based pyramid. Now take away the top corner

using a rubber and redraw it to look as though someone had cut it away.

(b) Complete the following for the remainder of the shape.

F =……….. V = …………. E = ………….

F + V – E = …………….

4. Here are some views of geometrical solids of the type drawn in class. State which they could

be. [Some will have more than one answer!]

(i) (ii) (iii) (iv)

5. This is a cuboid (edges not equal in length) and

shows a plane of symmetry.

i) Use tracing paper to copy the outline and

dotted (hidden) lines into your exercise book.

On your diagram draw a different plane of

symmetry.

ii) Repeat the exercise in (i) and draw another

different plane of symmetry.

6. This is a cube (all edges equal). It will have three

planes of symmetry similar to the cuboid in

question 1.

Shown is another plane of symmetry.

i) Use tracing paper to copy the outline and

dotted lines into your exercise book. Draw a

new plane of symmetry.

ii) Repeat the exercise of (i) as many times as

you need to until all planes of symmetry

have been found.

iii) How many planes of symmetry does the

cube have?

7. This is a square based pyramid and shows a plane of

symmetry.

i) Use tracing paper to copy the outline and dotted

lines into your exercise book. Draw a new plane of

symmetry.

ii) Repeat the exercise of (i) as many times as you

can have until all planes of symmetry have been

found.

8. This is a sphere with a plane of symmetry. Draw a

sphere into your book along with another plane of

symmetry.

How many planes of symmetry could be drawn?

9. This is a cylinder with a plane of symmetry.

Draw a cylinder into your book with a different plane of symmetry.

How many planes of symmetry could be drawn?

10. (i) Using a square (side 2cm) complete a net for a square

based pyramid each edge of which will be length 4 cm.

(ii) Draw on card a net for a square based pyramid of length

4cm. Add suitable flaps, cut out your net and glue together.

11. This is a sketch of a net for a regular tetrahedron, the

dotted lines indicating folds. Construct on card an

equilateral triangle of side 8 cm and mark the midpoints.

Join the midpoints with dotted lines. Draw some flaps. Cut

out your net; Use a pritt stick to glue together in the form

of a regular tetrahedron, each edge of which should be of

length 4 cm.

Geometry (12) Angles

1. The straight line

Work out the lettered angles for each of the following diagrams.

Remember to show your working. All diagrams are not drawn to scale.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18. 19.

45 a 110 b 20 c

107 d 27 e

148

f

20

g 45 29 h

36

i 102

47 j

61 42

m 77 54 k 89

2m m 2n

n

n 36 p 2p

q

q

100

r r

r

12

2t

4t

63

u

2u


2. Angles at a point

Work out the lettered angles for each of the following diagrams.


1. 2. 3.

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

80 a

130

100 b

190

95 c

155

120 d

90

40

72

e 67

88

104

f

94

87

57 g

35

116 40

h

81 77

i

95 131

i

k

72 85

2k

2m

167 88

m n

71

161

3n

p

44 27

p

107 2q

87

93

q q

r

114

3r 2r

Geometry (14) Opposite angles

Work out the lettered angles for each of the following.

Remember to show all working.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

35 a c

b 85 e

f

d

167

i

g

h

j k

l

m

21

p

q

94

s r

98

35

t u 40

104

w v 17

115

y

x

34

x a

z z

z

b c

e

d

81

68

2m

m m

p

56

2n

n

27

q

f m

j

l h k

g

i

79

127

84

95


Corresponding angles

Work out the lettered angles for each of the following.

Remember to show all working.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

70 f

e

d

55

c b

110

a

j 113

i

g

h

m

n

k

46

r

p q

37

u

v w

125

x

y z

138 t

s

68

a

c b 91

d

f

e

117

h

g

57

87

k

j i

103 79 m

n

66

r

q

p

75


Alternate angles

Work out the missing angles in each of the following triangles.


1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

60

a

b

115

37

c

e

d

g

98

h

f

65

m k

139

i

j

126

n

q

p

117

r t s

48

u v

51

w

x 74

a b

33

y

z


Angles in a triangle

Work out the missing angles in each of the following triangles.


1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. Two sides of a triangle measured 43 and 31, what is the size of the third side?

14. Kamran measured the angles of a triangle as 59, 86 and 37. Are the measurements likely to

be correct on this evidence?

15. In a right-angled triangle one angle is 8. What is the size of the other angle?

16. What are the sizes of the angles in a triangle with all equal angles?

17. The three angles in a triangle are given by x , x + 24 and x + 51. What is the value of x?

a

35

80 c

67

71

b

40 65

f

23 122 d 27

56 e

72 72

g

38

77

h

57

51

i 18

34

k k+10 42

m

m+80

3n

2n

n

2i


1. Work out the missing angles for each of the following:

(a) (b) (c)

(d) (e) (f)

2. For each of the following isosceles triangles find the missing angles.

(a) (b) (c) (d)

(e) (f)

3. Calculate the missing angles for each of the following parallelograms

(a) (b) (c)

a

b 65

c

d 47 e f

36

g h

13

i j

118 k

l

38

72 a

c b 54

d

f

e

115 h

g

i

105

a

38 b c

47

25 g

56

129 e f

h 31

i

131 k

8

164 l m

87 142

(d) (e) (f)

(g) (h)

4. Showing your working determine which of the following are sets of parallel lines.

(a) (b) (c)

(d) (e)

64

j

l

k

69

p

17

54

n

m 56

r q

45

t 69

s

u v

52 9

73

x w

24

81

81 146

36 115

85

112

23

157 68

Geometry (19) Area of a circle

Look at circle 1 on the 1 cm squared paper.

Its radius 3r cm 92 r

We estimate its area as follows:

(i) Number of whole squares = 16 cm2

(ii) Number of part squares = 10 cm2

Total = 26 cm2

Now using the calculator 9.2....88888.29

262

r

A

Record this information in your exercise book as shown above.

Repeat this exercise for the other drawn circles and record the information in your book in the

same way.

When you have completed this task, draw up and complete a table as follows:

Circle 1 2 3 4 5 6

2r

A

2.9

What conclusion can you draw?

r=2

r=4

r=3

Geometry (20) Area of a circle

1. Calculate the area for each of the following circles, giving your answers correct to 1 decimal

place.

(a) (b) (c) (d)

2. Calculate the area of each of the following circles giving your answers correct to 2 decimal

places.

(a) (b) (c) (d)

3. Which has the greater area, a circle with radius 5cm or a square with side 4cm?

4. Which has the greater area, a rectangle with dimensions 5m by 6m or a circle with diameter

10m?

5. Find the area of the semicircle drawn opposite,

giving your answer to 2 decimal places.

6. Find the area of the shape opposite, giving your

answer correct to 1 decimal place.

7. Calculate the shaded area for each of the following shapes. [giving your answers correct to 2

significant figures]

(a) (b) (c)

8. A circle has an area of 15 cm2. Calculate the length of its radius, giving your answer to 2

decimal places.

8m 12cm 12cm 30m

3.2m 5.4cm 79m 40km

24 cm

48 cm

27 cm

10cm 5cm 4m 9cm

15cm

2cm

Geometry (21) Circumference of a circle

1. Calculate the circumference of each of the following circles, giving your answers correct to one

decimal place.

(a) (b) (c) (d)

2. Calculate the circumference of each of the following circles, giving your answers correct to 2

decimal places.

(a) (b) (c) (d)

3. Find the perimeter of the semicircle drawn opposite,

giving your answer to 2 decimal places.

4. (a) What is the perimeter of a circle of diameter 60 metres (correct to 3 decimal places)?

The diagram is of a running track with “straights” of

length 120m and with semicircular ‘bends’ which have

diameter 60m.

(b) What is the length of one complete lap?

(c) How many laps (approximately) must an athlete run in a race of 10 000m?

5. A bicycle wheel has diameter 80cm. Calculate its circumference, giving your answer correct to

the nearest whole number.

6. What is the diameter of a circle whose circumference is 12cm? [Give your answer correct to 1

decimal place].

7. What is the area of a circle whose area is 40cm2? {give your answer correct to the nearest

whole number]

8. Which has the greatest perimeter, a circle with radius 5cm or a square with side 5cm?

3cm 12m 18cm 54m

4.1m 6.3cm 79m 37m

40 cm

120m

60m

Geometry (22) Volume of a prism

1. Without a calculator find (a) the base area (b) the volume for the following cuboids

(i) (ii) (iii) (iv)

(v) (vi) (vii) (viii)

2. A concrete beam is 14.3 metres long, 6.5 metres wide and 3.2 metres high. Find how many

cubic metres of concrete was used to make the beam.

3. A classroom has a volume of 3m210 , if the length and width of the room are 8m and 7.5m

respectively, how high is this classroom?

4. Bricks with dimensions 25cm by 12cm by 9cm are being used to build a wall.

(a) Find the volume of one brick (i) in 3cm (ii) in 3m .

(b) If the wall is to have a total volume of 60.75 3m , how many brick will we need ?

5. Without a calculator find the volume for each of the following triangular based prisms.

(a) (b) (c)

(d) (e) (f) (g)

18cm

7cm

9cm

5m 4m

9m

13m

6m

7cm

6cm

15cm 6cm

7cm

12cm

9cm 5m

3m

7m

15cm

13cm

11cm

17m

22m

26m

3cm

6cm

5cm

2m 10m

3m

3m

3m

7m

2m

6m

4m

2cm

7cm

5cm

5m

3m

8m

11cm

4cm

6cm

6. Workout the volume for each of the following, giving your answers to 2 decimal places.

(a) (b) (c) (d)

(e) (f) (g) (h)

7. For each of the following calculate

(i) the base area (ii) the volume, given that all measurements are in cm.

(a) (b) (c)

(d) (e)

10cm

15cm

12cm

5cm

4m

17m

7cm

10cm

8.4m

9.5m

3cm

6cm

4m

3.3m

8.6cm

7.5cm

7

9

5

6

3

5

6

9

11

5

3

4 10

7

12

7

9

8

8

10

20

15

Geometry (23) Reflections

Exercise 1

The dotted line is the mirror line. Draw the reflection of each object in the mirror line. Use a

coloured pen to draw the image.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

Exercise 2

2. Draw the image of ABC after

a reflection in the -axis.

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6 A B

D C

B

A C

3. Draw the image of PQR after


-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

4. Draw the following image after


-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6



-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6



-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

P

Q

R

1. Draw the image of ABCD after


-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7. Draw the image of the following

after a reflection in the line .

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


after a reflection in the line

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6



-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6



-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6



-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6



-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

Geometry (24) Rotations

Exercise 1

In each of the following questions draw the image of the given object under a rotation about P and

the angle described.

1. 90 anticlockwise 2. 180 3. 90 Clockwise

4. 90 Clockwise 5. 180 6. 90 Anticlockwise

7. 90 anticlockwise 8. 180 9. 90 Clockwise

10. 90 Clockwise 11. 180 12. 180

P

P

P

P

P P

P

P

P

P

P

P

Exercise 2

1. Draw the image of the following after

a rotation of clockwise centre (0,0)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

2. Draw the image of the following after a

rotation of centre (0, 0)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


rotation of anticlockwise centre (0,0)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


rotation of clockwise centre (-1, -2)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


rotation of clockwise centre (1, -1)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


rotation of centre (2, 0)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


a rotation of clockwise centre (1, 3)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


rotation of centre (-1, -2)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


a rotation of clockwise centre (2, 0)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


rotation of centre (1, -1)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


rotation of anticlockwise centre (-2, 2)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6


rotation of clockwise centre (2, 4)

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

Geometry (25) Enlargements

1. Enlarge the shape below by a scale factor of three centre of enlargement O. Label the image P’.

2. Draw shape ABCD after an enlargement with scale factor 2 centre D. Label the image A1B1C1D1.

3. Enlarge the triangle LMN by a scale factor 4 centre P.

O

P

A

B C

D

P

L

N

M

4. The object L has been enlarged onto Image L’.

(a) Identify the centre of enlargement and label it C.

(b) State the scale factor of the enlargement.

5. Obtain the centre and scale factor of the enlargement drawn below.

L L’

Geometry (26) Enlargements 2

TAKE CARE THAT PLENTY OF ROOM IS LEFT FOR THE FOLLOWING ENLARGEMENTS!

1. For each of the following state (i) the centre of enlargement

(ii) the scale factor of the enlargement.

(a)

(b)

1 0 2 4 3 6 5 7 9 8 10 11

1

2

3

4

5

6

7

8

9

x

y

1 0 2 4 3 5 7 6 8 9 17 18 19 16 15 14 13 11 10 12 x

y

1

2

3

4

5

6

7

8

9

10

(c)

(d)

2. Enlarge LMN by a scale factor of 2 centre (0, 0); Label the image L1M1N1

1 0 2 4 3 6 5 7 9 8 10 11 x -11 -10 -8 -9 -6 -7 -5 -3 -4 -2 -1

1

2

3

4

5

6

7

8

9

y

-9 -8 -6 -7 -5 -3 -4 -2 -1 7 8 9 6 5 4 3 1 2 x

y

-6

-5

-4

-3

-2

-1

1

2

3

4

-1 -2 1 2 3 4 5 6 7 -3 8 x

y

-2

-1

1

2

3

4

5

0

M

L

N

3. Enlarge ABC by a scale factor of 4 centre (3, 2). Label the image A1B1C1

4. Enlarge the object below with centre (-1, 1) by a scale factor 3.

5. Enlarge the object by a scale factor of 3 centre of enlargement (2, 1)

6. (a) Plot the points A(1, 2) , B( 3, 2) and C(3, 0) and join up the points to form a triangle ABC.

(b) Enlarge the triangle ABC by a scale factor of 2 centre (1, 3)

7. (a) Plot the points P(–2, –1) , Q(–2 , 2) and R(2, 1) and join up the points to form a triangle

PQR.

(b) Enlarge the triangle PQR by a scale factor of 3 centre (–1, –1)

-1 -2 1 2 3 4 5 6 7 -3 8 x

y

-2

-1

1

2

3

4

5

0

-1 -2 1 2 3 4 5 6 7 -3 8 x

y

-2

-1

1

2

3

4

5

0

-1 -2 1 2 3 4 5 6 7 -3 8 x

y

-2

-1

1

2

3

4

5

0

A

C

B

Geometry (27) Translations

1. The diagram drawn opposite shows four triangles

drawn in different positions.

Using the vector notation describe the translation

which will map

(i) ABC onto EDG

(ii) ABC onto HIJ

(iii) ABC onto PQR

(iv) PQR onto EDG

(v) HIJ onto PQR

2. Using the drawn triangle opposite

i) draw the image A’B’C’ after a translation of

ABC by

1

6

ii) draw the image A’’B’’C’’ after a translation of

ABC by

2

3

iii) draw the image A’’’B’’’C’’’ after a translation

of ABC by

1

4

3. (a) On a set of axes draw the shape STUV with coordinates S(2, 0) , T(5, 0) , U(5, 3) and

V(3, 3).

(b) Draw the image of STUV after a translation of

4

5. Label the image S’T’U’V’.

4. (a) On a set of axes draw the shape LMN with coordinates L(2, 1) , M(5, –2) , and N(3, 3).

(b) Draw the image of LMN after a translation of

4

4. Label the image L’M’N’.

(c) Draw the image of L’M’N’ after a translation of

7

1. Label the image L’’M’’N’’

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

A

B C

E

D G

H

I J P

Q R

-6 -5 -4 -3 -2 -1 1 2 3 4 5

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

A

B C

Geometry (28) Pythagoras Theorem

1. Work out the length of the hypotenuse for each of the following, giving your answers correct to 1

decimal place. [all measurements are in centimetres]

(a) (b) (c)

(d) (e) (f)

(g) (h) (i) (j)

Work out the required lengths for each of the following, giving your answers to 2 decimal places.

2. Find a 3. Find b

4. Find AC 5. Find EF

6. Find PR 7. Find LM

2

7

6

6 9

8

4

9

7

5

4

6

3

14 13

5

11

10

21

8

a b

c

d e

f

g

h

i j

7cm

9cm

a 5cm

11cm

b

16cm

10cm

A

C B

12cm

15cm

D

E

F

7cm 7cm

R

P

Q 6.3m

4.5m

L

M N

8. Find p 9. Find x

10. Find AC

11. Find the length of the diagonal in the rectangle below:

12. Find the sloped edge, XY, on the isosceles triangle drawn below.

13. A ladder is placed up against the side of a house so that it reaches a height of 12m. If the

distance from the foot of the ladder to the base of the house is 2m, what is the length of the

ladder?

5.9cm

14.3cm

p

10.5m

9.8m

A

C B

17 cm 20cm

x

10 cm

30 cm

X

Z

Y

10 cm

8 cm

Geometry (29) Pythagoras Theorem II

1. Work out the length of the lettered side for each of the following, giving your answers correct

to 1 decimal place. [all measurements are in centimetres]

(a) (b) (c)

(d) (e) (f)

(g) (h) (i) (j)

Work out the required lengths for each of the following, giving your answers to 2 decimal places.

2. Find m 3. Find p

4. Find AB 5. Find DE

6. Find PQ 7. Find MN

12 6

a

8

11 c

9

4

b

7

10 f

13

5

e 3

6

d

3

14

j 18

7

h

15

10

i

20

6

g

15cm

12cm

m 5cm

11cm

p

8cm

10cm

A

C B

25cm 15cm

D

E

F

14cm

7cm

R

P

Q

8.1m 3.7m

L

M N

8. Find c 9. Find x

10. Find JK

11. Find the height of the isosceles triangle drawn below.

3. A ladder, of maximum length 5.4m, is placed up against the side of a house. If the distance

from the foot of the ladder to the base of the house is 2m, how high up the side of the house

will the ladder reach?

5.9cm 14.3cm

c

10.5m

5.4m

J

L K

13 cm

19cm

x

16 cm 16 cm

S

U

T

h cm

10 cm

Geometry (30) Bearings I

1. Write down the bearings of A from B for each of the following diagrams.

(a) (b)

(c) (d)

(e) (f)

(g) (h)

A

B

N

A

B

N

A

B

N

A

B

N

A

B

N

A

B

N

A

B

N

A

B

N

2. Write down the bearings each of the following demonstrates

(b) (b)

(c) (d)

(f) (f)

(g) (h)

X

Y

N

K

J

G

F

N

C

D

N

T

S

N

U

V

N

N

M

N P

Q

N

Geometry (31) Bearings II

1. Draw an accurate diagram to represent each of the following bearings.

(a) B is on a bearing of 056 from A

(b) C is on a bearing of 143 from D

(c) L is on a bearing of 078 from M

(d) H is on a bearing of 162 from J

(e) A is on a bearing of 197 from B

(f) X is on a bearing of 233 from Y

(g) E is on a bearing of 259 from D

(h) V is on a bearing of 297 from U

(i) P is on a bearing of 316 from Q

(j) W is on a bearing of 348 from Z

2. Town B is 6 km from town A on a bearing of 076. Town C is 5 km from Town A on a bearing of

154. Using the scale 1 cm represents 1 km, draw a scale drawing to show Towns A, B and C.

How far is town B from town C?

On what bearing is town B from town C?

3. A ship, S, sails a distance of 4km on a bearing of 056 and then a further 4km on a bearing of

097. Using the scale of 1 cm represents 1 km, draw a scale drawing of this journey.

How far is the ship away from its original position?

On what bearing could the ship have originally taken?

4. The insert given shows the towns of Appleton, Barton, Cotley, Dove and Eccles.

Using the diagram work out the bearing of

(a) Eccles from Appleton

(b) Cotley from Dove,

(c) Dove from Barton,

(d) Appleton from Cotley,

(e) Barton from Eccles.

5. Using the second insert a ship is spotted from the two lighthouses shown. The first lighthouse,

P, states that the ship is on a bearing of 081 while the second lighthouse, Q, states that the

ship is on a bearing of 315. Using a suitable construction identify on the insert the position of

the ship.

Geometry (31) Inserts

Insert 1

Insert 2

Appleton

Q

Barton

Dove

Eccles Cotley

P

geometry workbook

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