4
Unit
GEOMETRY
In this topic, pupils will learn to apply their skills and concepts to analyse mathematical situations, make connections among mathematical ideas and express them logically in the following areas: • Perpendicular and parallel lines • Angles: right angles, angles on a straight line, vertically opposite angles and angles at a point • Properties of a square, a rectangle, a triangle, a parallelogram, a rhombus and a trapezium • 8-point compass
Numbers that make sense Read each problem. Then, place the numbers from the box into the blanks where you think they fit best. Read the problem again and see if the numbers make sense. 1
58
60
62
∠a is smaller than ∠b . ∠a = ∠b =
°, ∠c =
∠d =
°.
°, ° and
How would you check that the numbers are in the correct places? Write a short explanation below.
Mathematics Problems…
SOLVED!
d
a
56
118
Book C
c b
Hint ∠d is equal to the sum of which two angles ?
Unit 4 2
45
60
75
135 e
The ratio of ∠e : ∠f is 3 : 1. ∠g is 30° greater
than ∠f . ∠e = ∠g =
°, ∠f =
°,
° and ∠h =
°.
f
h g
How would you check that the numbers are in the correct places? Write a short explanation below.
Hint What is th e sum of ∠e and ∠f ?
3
56
59
62
is smaller than
∠b
∠c
. ∠b is greater than ∠a by
°. ∠c is bigger than ∠a by ∠a =
°.
c
°.
How would you check that the numbers are in the correct places? Write a short explanation below.
a b 59°
Geometry
57
4
∠d
∠e
23
37 . ∠d =
is bigger than ∠e =
83
° and ∠f =
°,
f
°. d
46°
e
How would you check that the numbers are in the correct places? Write a short explanation below.
5
∠g
∠h
The ratio of
∠i :
69 = 1 : 2.
= 32°. The sum of ∠g and ∠h =
°. ∠i =
74
°.
58° 21°
g
h
How would you check that the numbers are in the correct places? Write a short explanation below.
58
Mathematics Problems…
SOLVED!
Book C
i
Unit 4
The wrong answers Read each problem and identify what is wrong with each answer. Then write down how you would get the correct answer in the space provided. 1 Find the value of ∠j .
j
∠j = 90° + 49° = 139°
Explain briefly what is wrong with the solution provided. Then solve the problem and provide the correct solution.
49°
2 JK and LM are straight lines. The ratio of ∠x and ∠y is 4 : 5.
Find the value of ∠z .
9 units = 180°
1 unit = 20°
∠z
Explain briefly what is wrong with the solution provided. Then solve the problem and provide the correct solution.
= 6 units = 120°
J
y
L
x M
z K Hint Whic h two angle s are vertica lly opposite?
Geometry
59
3 Find the value of ∠j .
180° – 156° = 24°
∠j
j
= 180° – 24° = 156° 156°
Explain briefly what is wrong with the solution provided. Then solve the problem and provide the correct solution.
4 Find the value of ∠k .
141°
∠k = 141° – 60° = 81°
k
Explain briefly what is wrong with the solution provided. Then solve the problem and provide the correct solution.
60
Mathematics Problems…
SOLVED!
Book C
Unit 4 5 Find the difference between ∠m and ∠n .
∠m = 90° – 41° = 49°
∠n = 90° – 51° = 39°
∠m – ∠n
= 49° – 39°
= 10°
Explain briefly what is wrong with the solution provided. Then solve the problem and provide the correct solution.
51°
41°
m
n
6 The figure shown is not drawn to scale. Find the value of ∠a .
∠a = 180° – 90° – 59°
= 31° a
59°
Explain briefly what is wrong with the solution provided. Then solve the problem and provide the correct solution.
Geometry
61
7 The figure shown is not drawn to scale. Find the value of ∠b .
∠b = 140° – 60°
b
= 80°
140°
Hint What is the value of each angle of an equilateral tr iangle?
Explain briefly what is wrong with the solution provided. Then solve the problem and provide the correct solution.
8 The figure shown is not drawn to scale. Find the value of ∠c .
∠c = 115° + 42°
Explain briefly what is wrong with the solution provided. Then solve the problem and provide the correct solution.
62
= 157°
Mathematics Problems…
SOLVED!
Book C
115°
42°
c
Unit 4
Writing your own word problems In the boxes provided, write two questions based on the information provided. J
L
1 ∠JPM = 65° and
P
∠PQK = 40°. M
K Q Question (a)
Question (b)
Write the answers to your two questions in the boxes below. Answer (a)
Answer (b)
Geometry
63
2 ∠ABC = 50°.
A
B
C
Question (a)
D
Question (b)
Write the answers to your two questions in the boxes below. Answer (a)
Answer (b)
64
Mathematics Problems…
SOLVED!
Book C
Unit 4 3 The figure shown is not drawn to scale. R
S
P 56°
56°
T
Q
Hint Wh ich two a are equal? ngles
Question (a)
Question (b)
Write the answers to your two questions in the boxes below. Answer (a)
Answer (b)
Geometry
65
4 The figure shown is not drawn to scale. B
A 41°
D
C
Question (a)
Question (b)
Write the answers to your two questions in the boxes below. Answer (a)
Answer (b)
66
Mathematics Problems…
SOLVED!
Book C
Unit 4
Writing questions to answers Write the question to each answer that is given.
1
D
E
63° A
B
C
(a) Answer: 90°
(b) Answer: 117°
(c) Answer: 27°
(d) Answer: 180°
Geometry
67
A
2 H
B
G
C
F
D E
(a) Answer: Southeast
(b) Answer: G
(c) Answer: 225°
(d) Answer: Anti-clockwise
68
Mathematics Problems…
SOLVED!
Book C
Unit 4 M
3
65째
I K
L
J
(a) Answer: 65째
(b) Answer: 130째
(c) Answer: 40째
(d) Answer: 8 : 13
Geometry
69
4
M
N
O 121°
49°
R
S
Q
P
(a) Answer: 59°
(b) Answer: 72°
(c) Answer: 49°
(d) Answer: ∠OPQ and ∠RQS
70
Mathematics Problems…
SOLVED!
Book C
Unit 4 5 The figure shown is not drawn to scale. A 41°
58° D
B
e
g
f 76°
d C o angles are Hint Which tw angles equal? Which ? add up to 180°
(a) Answer: 81°
(b) Answer: 23°
(c) Answer: 122°
(d) Answer: 35°
Geometry
71
6 ABCD is a parallelogram, not drawn to scale. A
D
j
h
g
69° B
i E
C
(a) Answer: 42°
(b) Answer: 69°
(c) Answer: 27°
(d) Answer: 15°
72
Mathematics Problems…
SOLVED!
Book C
Unit 4 7 The figure shown is not drawn to scale.
52°
76°
k m
n
p
(a) Answer: 76°
(b) Answer: 52°
(c) Answer: 24°
(d) Answer: ∠m and ∠n
Geometry
73