year 7 - pbworksthomaswhitham.pbworks.com/f/geometry year7.pdf17cm 16cm 27cm 8cm 13m 13m 5m 15m 18cm...
TRANSCRIPT
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
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.
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.
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
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
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.
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.
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
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
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
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
Geometry (8) Angles
1. Using a protractor measure each of the following angles.
A
B C
D E
F
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
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
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
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.
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
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
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
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
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
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
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
(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
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.
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
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
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
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)
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
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
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)
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 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.