Year 7 - PBworksthomaswhitham.pbworks.com/f/Geometry year7.pdf17cm 16cm 27cm 8cm 13m 13m 5m 15m 18cm...

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Thomaswhitham.pbworks.com Year 7 Geometry Year 7 THOMAS WHITHAM SIXTH FORM

Transcript of Year 7 - PBworksthomaswhitham.pbworks.com/f/Geometry year7.pdf17cm 16cm 27cm 8cm 13m 13m 5m 15m 18cm...

Page 1: Year 7 - PBworksthomaswhitham.pbworks.com/f/Geometry year7.pdf17cm 16cm 27cm 8cm 13m 13m 5m 15m 18cm 21cm 5cm 12cm 13cm 22cm 11cm 6cm 9cm 15cm 23cm 3m 8cm 21cm 8cm 3m 3m 18m 9m 7m

T h o m a s w h i t h a m . p b w o r k s . c o m

Year 7

Geometry Year 7

THOMAS WHITHAM SIXTH FORM

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Geometry (1) Estimation & Measurement

Exercise 1

Copy and complete the diagram and sentences.

For each sentence you must give an estimated measurement.

Myself

1. I am ………… cm tall.

2. The distance around my head is

……. cm

3. My arm is …….. cm long.

4. My hand span is ……… cm

5. The distance around my wrist is

…….. cm

6. The distance around my chest is

…….. cm

7. The distance around my waist is

……… cm

8. The distance between my knee

and the floor is ……… cm

9. My shoe is …….. cm long

10. My weight is ……… kg.

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Exercise 2

NOW YOU WILL NEED A RULER, SOME STRING OR TAPE MEASURE AND SOME SCALES.

Copy and complete the diagram and sentences.

For each sentence you must give an accurate measurement.

Myself

11. I am ………… cm tall.

12. The distance around my head is

……. cm

13. My arm is …….. cm long.

14. My hand span is ……… cm

15. The distance around my wrist is

…….. cm

16. The distance around my chest is

…….. cm

17. The distance around my waist is

……… cm

18. The distance between my knee

and the floor is ……… cm

19. My shoe is …….. cm long

20. My weight is ……… kg.

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Geometry (2) Estimation and measuring objects

To answer the following questions look at the pictures given on the additional sheet.

1. Estimate the length of:

a) the scissors

b) the smallest key on the key-ring

c) the width of the calculator

d) the length of the pen

e) the length of one button on the

calculator

2. Using your ruler, what is the length of

a) the pencil

b) the largest key on the key-ring

c) the key-ring

d) the calculator

e) the scissors

3. The compass is set to draw a circle. Estimate the radius of the circle the compasses are set to

draw.

4. Estimate the dimensions for the piece of paper, which contains the objects, described above.

5. Estimate the length of

a) the telephone

b) the sunglasses

c) the piece of chalk

6. Without using a ruler what are the approximate dimensions for

a) the stamp

b) the envelope

7. Estimate the diameter of the number buttons on the telephone.

8. Using your ruler measure the lengths of

a) the stamp

b) the sunglasses

c) the telephone

d) the envelope

e) the glass lens in the envelope

f) the aerial on the telephone

g) the piece of chalk

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Geometry (3) Perimeter

Work out the perimeter for each of the following rectangles.

1. 2. 3.

4. 5. 6.

7. 8. 9.

Work out the perimeter for each of the following shapes.

10. 11. 12.

13. 14. 15.

19cm

15cm

15 cm

8 cm

7 cm

11 cm

38cm

11cm

17cm

16cm

27cm

8cm

13m

13m

5m

15m

18cm

21cm

5cm

12cm

13cm

22cm

11cm

6cm

9cm 23cm 15cm

8cm

21cm

8cm

3m

3m

3m 18m

9m

7m

9m

9m

9m

9m

9m

9m

14m

6m

8m

6m

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Estimate in each case the area enclosed by each of the irregular shapes. Answers in squared

units. [Also give a brief description to the method used]

11. 12.

13. 14.

15.

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Geometry (4) Area by counting squares

Find the area in unit squares of each of the following shaded regions.

1. 2.

3. 4.

5.

6. 7. 8.

9.

10.

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Geometry (5) Area of rectangles

Work out the area for each of the following rectangles.

2. 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

10m

10m

5m

15m

4m

5m

14m

23m

4m

19m

21mm

27mm

28cm

27cm

32cm

23cm

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Geometry (6) Area of triangle

Work out the area for each of the following triangles.

3. 2. 3.

4. 5. 6.

7. 8. 9.

10. Find the area of the following triangles.

(a) (b) (c)

(d) (e) (f)

7cm

12cm

8 cm

9 cm

4 cm

7 cm

20cm 6cm

8cm

5m 8mm

15mm

5m

14m

17cm

6m 14m

24m

6cm

8cm

6cm

7cm

11cm

13cm

48m

37m

86cm

129cm

17m

63m

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Geometry (7) Constructions

1. Using point C as centre draw two circles,

one with radius 2.5cm radius the other

with 4.0cm radius.

Draw any diameter of the larger circle and

label the ends A and B. Label the points

P and Q where AB cuts the smaller circle.

What is the length of AP?

AP = ...................

2. Draw a circle of radius 3cm with centre A, and a circle of radius 4cm with centre B. Label the

points of intersection of the two circles P and Q. Join P to Q with a straight line and measure the

length of PQ; write your answer in the space below.

PQ= ...................

3. Draw a line 6cm long and label it AB. Construct a circle which has AB as diameter.

C

A B

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4. Draw a circle centre A with radius 3cm. Choose a point on the circumference of this circle and

label it B. With B as centre draw a second circle of radius 3cm. Label the points of intersection of

these two circles P and Q. Draw a circle centre P of radius 3cm and label its intersections with

the other two circles X and Y. Draw a straight line joining X and Y.

5. Draw a semicircle which has diameter ST.

A

S T

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Geometry (8) Angles

1. Using a protractor measure each of the following angles.

A

B C

D E

F

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2. Use a protractor, a ruler and a sharp pencil to draw angles of these sizes.

(a) 40 (b) 130 (c) 95 (d) 134 (e) 157 (f) 193 (g) 76

(h) 84 (i) 122 (j) 265

3. What type of angle is each of the following?

G H J

a

b

c

d

e

f

g

h i

j

k l

m n

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Geometry (9) 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

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Geometry (10) Construction of triangles

REMEMBER DO NOT REMOVE ANY CONSTRUCTION LINES OR ARCS.

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 a triangle PQR where PQ = 3 cm , 135 = RQP and 20 = RPQ .

Measure and write down the length of side QR.

6. Draw a triangle BCD where BC = 8.4 cm , 36 = DCB and 49 = DBC .

Measure and write down the length of side BD.

7. Draw a triangle HIJ where HI = 6.7 cm , 74 = JHI and 58 = JIH .

Measure and write down the length of side IJ.

8. Draw a triangle ABC where AB = 5 cm , 121 = CBA and 33 = CAB .

Measure and write down the length of side AC.

9. Draw a triangle DEF where DE = 7.3 cm , 47 = FDE and 29 = FED .

Measure and write down the length of side DF.

10. Draw an accurate drawing of the triangle opposite.

4.6 cm

24 107

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Geometry (11) Construction of triangles

REMEMBER DO NOT REMOVE ANY CONSTRUCTION LINES OR ARCS.

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 = ZXY ˆ 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.

6. Draw the triangle DEF where DF = 5.3 cm, DFE = 63 and FE = 6.4 cm.

Measure and write down the size of FDE .

7. Draw a triangle STU where ST = 10.7 cm , 13 = UST ˆ and SU = 8.5 cm.

Measure and write down the length of TU.

8. Draw the triangle EFG where EF = 9.4 cm, 28 = GFE ˆ and FG = 6.7 cm.

Measure and write down the size of EGF ˆ .

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

State the length of the diagonal AC.

10. Construct a rectangle that has dimensions 5.3cm by 11.7cm.

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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

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Geometry (13) Angles

2. Angles at a point

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.

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

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Geometry (14) Angles

3. 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

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Geometry (15) Angles

4. 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

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Geometry (16) Angles

5. Alternate angles

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

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

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

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Geometry (17) Angles

5. Angles in a triangle

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

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. 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

34

k k+10 42

m

m+80

3n

2n

n

i 18

2i

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Geometry (18) Transformations: Reflections

1. Reflect each of the following in the given mirror line to produce a letter of the alphabet.

2. Complete the reflection given below to produce a two-digit number.

3. Reflect the face below in the given mirror line to produce the face of your favourite maths

teacher!

4. Copy each of the shapes below and draw in, where possible, any lines of symmetry that the

shape has.

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

A D H I

V

4 8

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

5. Draw each of the following letters and draw on, if any, lines of symmetry that each letter has.

L M Q U R

S T E F W

C X Y Z B

6. Which of the following numbers have lines of symmetry?

1 2 3 4 6 8 0

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Geometry (19) Transformations: 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.

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Exercise 2

1. Draw the image of ABCD after

a reflection in the x-axis.

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

2. Draw the image of ABC after

a reflection in the y-axis.

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

y

-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

a reflection in the x-axis.

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

4. Draw the following image after

a reflection in the y-axis.

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

5. Draw the following image after

a reflection in the x-axis.

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

6. Draw the following image after

a reflection in the y-axis.

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

P

Q

R

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7. Draw the image of the following

after a reflection in the y axis.

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

8. Draw the image of the following

after a reflection in the line y = x

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

9. Draw the image of the following

after a reflection in the x axis

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

10. Draw the image of the following

after a reflection in the x axis

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

11. Draw the image of the following

after a reflection in the line y = x.

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

12. Draw the image of the following

after a reflection in the line y = x

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

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Geometry (20) Transformations: 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

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13. Which of the following letters have rotational symmetry? State the order of rotational symmetry in

each case

A I T R O 14. State the order of rotational symmetry for each of the following shapes.

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

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

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7. Draw the image of the following after

a rotation of 90 clockwise centre (1, 3)

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

8. Draw the image of the following after a

rotation of 180 centre (-1, -2)

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

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

9. Draw the image of the following after

a rotation of 90 clockwise centre (2, 0)

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

y

-6

-5

-4

-3

-2 -1

1

2 3

4

5

6

10. Draw the image of the following after a

rotation of 180 centre (1, -1)

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

y

-6

-5

-4

-3

-2

-1

1

2 3

4

5

6

11. Draw the image of the following after a

rotation of 90 anticlockwise centre (-2, 2)

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

y

-6

-5

-4

-3

-2 -1

1

2 3

4

5

6

12. Draw the image of the following after a

rotation of 90 clockwise centre (2, 4)

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

y

-6

-5

-4

-3

-2

-1

1

2 3

4

5

6

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Geometry (22) Transformations: 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 x

y

-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 x

y

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

A

B

C

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Geometry (23) 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)

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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?

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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 the square (side 2cm) complete a net for a square

based pyramid each edge of which will be length 2 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.

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