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Pythagoras’ Theorem Student
Book - Series I-1
r
y x
Mathletics Instant Workbooks
Copyright ©
Pythagoras’ theorem Student Book - Series I Contents Topics
Date completed
Topic 1 - Hypotenuse of the right angled triangle
__/__/__
Topic 2 - Naming the sides of a right angled triangle
__/__/__
Topic 3 - Selecting the correct Pythagoras’ rule
__/__/__
Topic 4 - Squares, square roots and Pythagorean triads
__/__/__
Topic 5 - Finding the length of the hypotenuse
__/__/__
Topic 6 - Finding the length of one of the other sides
__/__/__
Topic 7 - Miscellaneous questions on Pythagoras’ theorem
__/__/__
Topic 8 - Problem solving and Pythagoras’ theorem
__/__/__
Practice Tests Topic 1 - Topic test A
__/__/__
Topic 2 - Topic test B
__/__/__
Author of The Topics and Topic Tests: AS Kalra
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
Chapter 2 Pythagoras’ theorem
EXCEL MATHEMATICS YEAR 8
pages 124–125
Topic 1: of the rightright angled triangle UNIT 1:Hypotenuse Hypotenuse of the angled triangle Question 1 Name the hypotenuse of each right angled triangle. a
a
B
b
C
c
P
q
b
n
m
r N
R A
d
L
c
e
T
R
S
l
Q
p
M J
f
W
U V
K
L
Question 2 Name the hypotenuse of the triangle named below in the diagram. a
A
B
b P
Q
E
D
∆ADC
d
L
M
T
C
S
T
e A
P
S
Q
R
∆PST
c
J R
K
N
∆PSR
∆LJM
f D
D
B
E
H
F ∆FHG
C
∆CBD
G
Question 3 Complete the following statements. a
is the length of the side opposite to angle D.
b
is the length of the side opposite to angle E.
c
is the length of the side opposite to angle F.
d
is the length of the hypotenuse of ΔDEF.
e
is the area of the square on the side opposite to ∠D.
f
is the area of the square on the side opposite to ∠F.
12
d
E
f
F
e D
EXCEL ESSENTIAL SKILLS: YEAR 8 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
1
Pythagoras’ theorem
EXCEL MATHEMATICS YEAR 8
pages 124–125
Topic the sides of aof right angled triangle UNIT 2: 2:Naming Naming the sides a right angled triangle
For each of the following triangles, complete the table below and that the square on the hypotenuse is equal to the sum of the squares on the other two sides. 5 1 B 2 A 3 C 5
3
10 13
C
A C
4
5
16
B
A
12
B
8
20
C 24
A
8
12
A
C
10
26
9
B
15
B 20
B
9
A 34 16
25
B
C
17
15
7
C
8
6
C
A
6
12
A
4
B
15
B 30
C A
a
b
c
a2
b2
c2
a2 + b2
1 2 3 4 5 6 7 8 9 13
Chapter 2: Pythagoras’ theorem
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
2
Pythagoras’ theorem theorem Pythagoras’
EXCEL MATHEMATICS YEAR 8
page 125
Topic thethe correct Pythagoras’ rule UNIT3:3:Selecting Selecting correct Pythagoras’ rule In the following right angled triangles, circle the correct statement. 1
a a2 = b2 + c2 b b2 = a2 + c2 c c2 = a2 + b2
A
7
S
a s2 = t2 + u2 b t2 = s2 + u2 c u2 = s2 + t2
T
C B
U D
a d2 = e2 + f 2 b e2 = d2 + f 2 c f 2 = d2 + e2
2
X
8
Y
F
E
Z G
3
a x2 = y2 + z2 b y2 = x2 + z2 c z2 = x2 + y2
H
a g2 = h2 + i2 b h2 = g2 + i2 c i2 = g2 + h2
U
9
a u2 = v2 + w2 b v2 = u2 + w2 c w2 = u2 + v2
V
W
I
a j 2 = k2 + l 2 b k2 = j2 + l 2 c l2 = j2 + k2
J
4
K
5
a b2 = c2 + d2 b c2 = b2 + d2 c d2 = b2 + c2
B
C
L
D
a m2 = n2 + o2 b n2 = m2 + o2 c o2 = m2 + n2
M
10
a e2 = f 2 + g2 b f 2 = e2 + g2 c g2 = e2 + f 2
11 E
O N
F
a p2 = q2 + r2 b q2 = p2 + r2 c r2 = p2 + q2
Q
6 P
G
12
H
a h2 = i2 + j 2 b i2 = h2 + j 2 c j 2 = i2 + h2
I J
R
14
EXCEL ESSENTIAL SKILLS: YEAR 8 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
3
Pythagoras’ theorem theorem Pythagoras’
EXCEL MATHEMATICS YEAR 8
pages 35–36, 125, 128–129
UNIT 4: 4:Squares, Squares, square roots Pythagorean Topic square roots and and Pythagorean triads triads Question 1 Use your calculator to find the following squares. a 152 =
b 132 =
c 402 =
d 282 =
e 52 =
f 692 =
g 102 =
h 172 =
i 812 =
j 82 =
k 412 =
l 992 =
Question 2 Use the square root key to find n. a n2 = 169
b n2 = 841
c n2 = 576
d n2 = 4761
e n2 = 100
f n2 = 1444
g n2 = 144
h n2 = 441
i n2 = 1600
j n2 = 2809
k n2 = 784
l n2 = 5625
Question 3 Which of the following are Pythagorean triads? a {2, 4, 6}
b {9, 12, 15}
c {9, 40, 41}
d {4, 6, 10}
e {3, 4, 5}
f {8, 13, 17}
g {8, 10, 12}
h {19, 40, 41}
i {6, 8, 10}
j {5, 12, 13}
k {15, 36, 39}
l {8, 15, 17}
Question 4 Prove that the following triangles are right angled triangles. a
5
4
5
12
b
3
13
15
Chapter 2: Pythagoras’ theorem
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
4
Pythagoras’ Pythagoras’ theorem theorem
EXCEL MATHEMATICS YEAR 8
pages 125–126
UNIT 5:Finding Findingthe the length of hypotenuse the hypotenuse Topic 5: length of the
Question 1 Find the length of the hypotenuse in each of the following. (All measurements are in centimetres.) a
b
x
15
20
4
x
3
c
6
d
8
x
e
30
12
16
x
5
f
24
10
x
x
Question 2 Find the length of the hypotenuse correct to one decimal place. (All measurements are in centimetres.) a
x
x
4
4.2
e
7
x
x
d
7
3
3.5
c
5
b
5
f
1.2 3.4
x
6.5
x
3.5
16
EXCEL ESSENTIAL SKILLS: YEAR 8 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
5
Pythagoras’ Pythagoras’ theorem theorem
EXCEL MATHEMATICS YEAR 8
pages 126–127
UNIT 6:Finding Findingthe the length of one ofother the other Topic 6: length of one of the sides sides
Question 1 In the following triangles, f ind the length of the unknown sides. (All measurements are in centimetres.) a
x
12
c
x
15
12
x
d
x
f
x
41
20
6
17
e
13
b
10
x
7
40
25
Question 2 Find the length of the unknown side correct to one decimal place. (All measurements are in centimetres.) a
x
15.3
6
b
x
14
8.9
c
d
5
e
x 14.2
x
4.5
9
x
17
f
12.3
15
7
x 17
Chapter 2: Pythagoras’ theorem
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
6
Pythagoras’ Pythagoras’ theorem theorem
EXCEL MATHEMATICS YEAR 8
UNIT 7: Miscellaneous Miscellaneous questions Pythagoras’ theorem Topic 7: questions on on Pythagoras’ theorem
pages 129–131
Question 1 In each of the following, fnd the length of the unknown sides (All measurements are in centimetres.) a
12
x
16
17
x
c
x
b
5
11
8
d
x
20
2
y
3
4
e
12
x
f
24
20
x 30
Question 2 Find the length of the unknown side correct to two decimal places. (All measurements are in centimetres.) a
b 5
x
6
3
x
12
14
c
d
7
x
6
10
x
4
e
18
x
f
5
24
x
15 21
EXCEL ESSENTIAL SKILLS: YEAR 8 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
7
Pythagoras’ Pythagoras’ theorem theorem
EXCEL MATHEMATICS YEAR 8
pages 131–132
UNIT 8:Problem Problem solving Pythagoras’ theorem Topic 8: solving andand Pythagoras’ theorem
1
Find the length of the diagonal of a square of side length 5 cm. ________________________________________
2
Find the length of the diagonal of a rectangle of length 35 cm and width 12 cm. ______________________________________________________________________________________________
3
What is the altitude of an equilateral triangle whose sides are each 16 cm long? Give your answer correct to two decimal places. __________________________________________
4
A 15 metre ladder rests against a wall and its foot is 4 metres away from the base of the wall. How high does it reach up the wall? Give your answer correct to two decimal places. ______________________________________________________________________________________________
5
The sides of a rectangle are 12 cm and 6 cm. Find the length of the diagonal. Give your answer correct to one decimal place. ______________________________________________________________________________________________
6
The hypotenuse of a right angled triangle is 30 cm. If one of the shorter sides is 18 cm, find the length of the other side. ______________________________________________________________________________________________
7
In a right angled triangle, the longest side is 39 cm and the shortest side is 15 cm. Find the length of the third side. __________________________________________________________________________________________________
8
a
Find the length of the unknown side in each of the following triangles, correct to two decimal places. (All measurements are in centimetres.) b
15
c
a
4 14
x
18
y
12
11
d
e
9
12
25
x
36
64
x
60
x 9
f
Find the perimeter of the triangle below (correct to one decimal place) by finding the hypotenuse first. 29 30
19
Chapter 2: Pythagoras’ theorem
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
8
Pythagoras’ theorem Pythagoras’ theorem Topic TOPICTest TEST Instructions Instructions
PART PART A A
This part consists of 12 multiple-choice questions • This part consists of 12 multiple choice questions Each question is worth 1 mark • Each question is worth 1 mark Fill in only ONE CIRCLE for each question • Fill in only ONE CIRCLE for each question Calculators are NOT allowed • Calculators may be used
Time allowed: allowed: 15 15 minutes minutes Time
Total marks =Total 12 marks = 12 Marks Marks
1
A triangle is said to satisfy the rule c22 = a22 + b22 for which special triangle? acute angled right angled obtuse angled
D none of these
1
The longest side of a right angled triangle is called the shortest side middle side hypotenuse
D none of these
1
Given that c22 = a22 + b22 and a = 8, b = 15, what is the value of c? 17 23 289
D 529
1
A 2
A 3
A 4
B B
1
1
If two sides of a right angled triangle are 2.4 m and 1 m then the hypotenuse is 2.4 m 2.6 m 3.4 m
D 3.8 m
1
The Pythagorean result for a triangle ABC right angled at C is a22 = b22 + c22 b22 = a22 + c22 c22 = a22 + b22
D none of these
1
The hypotenuse of a right angled triangle is opposite to the acute angle right angle obtuse angle
D none of these
1
A 9
B obtuse angled triangles D any triangle D
A 8
The hypotenuse of a right angled triangle is 17 cm. If one side is 15 cm, the third side is 14 cm 12 cm 10 cm 8 cm
A 7
C
Pythagoras’ theorem can be applied to acute angled triangles right angled triangles
A 6
C
B
A C 5
C
B B B
B
C C
C C
If two shorter sides of a right angled triangle are 7 m and 8 m, then the hypotenuse is 65 85 113 193
A
B
C
10 In a triangle ABC right angled at C, the hypotenuse is named as
A a
B b
C c
D
1
D none of these
1
11 If two sides of a right angled triangle are 6 cm and 8 cm, then the hypotenuse is
A 10 cm
B 9.4 cm
12 If n22 = 2304 then n equals
A 38
B 42
C 12 cm
D 14 cm
1
C 48
D 52
1
Total marks achieved for PART A 20
12
TotalYEAR marks achieved forAND PART EXCEL EXCEL ESSENTIAL ESSENTIAL SKILLS: SKILLS: YEAR 88 MATHEMATICS MATHEMATICS REVISION REVISION AND EXAM EXAMA WORKBOOK WORKBOOK 11
12
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
9
Pythagoras’ Pythagoras’ theorem theorem Pythagoras’ theorem TOPIC TOPIC TOPIC TEST TEST TEST Topic Test
PART PART PARTBBBB PART
Instructions Instructions Instructions • This part consists of 15 questions This part consists of 15 questions This part consists of 15 questions Instructions • • This part consists of 15 questions
Each question is worth 2 marks Each question is worth 2 marks Each question is worth 2 marks • • • Each question is worth 1 mark Write answers in the answers-only column Write answers in the answers-only column • ••Write answers in the answers-only column Write answers in the answers-only column ••Calculators may be used Calculators may be used Calculators may be used Time allowed: •20 minutes
Total marks = 15 Total Total Totalmarks marks marks===30 30 30 Answers only Marks Marks Marks Answers Answers Answersonly only only Marks
Time Time Timeallowed: allowed: allowed:15 15 15minutes minutes minutes Questions Questions Questions Questions
111 IfIf Ifn2nn2=2 ==3844 3844 3844then then thenfind find findthe the thevalue value valueofof ofnnn
QQ Q 3636 36
222 IsIs Is{6, {6, {6,8,8, 8,10} 10} 10}a aPythagorean a Pythagorean Pythagoreantriad? triad? triad? 333 Prove Prove Provethat that thatΔPQR ΔPQR ΔPQRisisisa aright a right rightangled angled angled
111
222
111
333
111
4 7.2 cm 7.2 cm 7.2 cm 44
111
555
111
666
111
777
111
888
111
999
111
10 10 10
111
11 11 11
111
12 12 12
111
13 13 13
111
14 14 14
111
15 15 15
111
2727 27
PPP
triangle. triangle. triangle.
111
RRR
4545 45
Find Find Findthe the thelength length lengthofof ofthe the theunknown unknown unknownside side sideinin inthe the thefollowing following followingtriangles triangles trianglescorrect correct correct toto totwo two twodecimal decimal decimalplaces. places. places. 444
555 3 m 3 m 3 m
22 m 22 m 22 m
666
x xx
9.6 cm 9.6 cm 9.6 cm
x xx
777
x xx
17 m 17 m 17 m
15 m 15 m 15 m
8887 cm 7 cm 7 cm
12 m 12 m 12 m
999
1 m 1 m 1 m
x xx
24 cm 24 cm 24 cm
13 m 13 m 13 m
2 m 2 m 2 m
x xx
x xx
3 m 3 m 3 m
10 10 10
11 11 11 13 m 13 m 13 m
x xx
5 m 5 m 5 m
12 12 12 x xx
8 m 8 m 8 m
12 m 12 m 12 m
x xx
11 m 11 m 11 m
13 13 13
14 14 14
8 cm 8 cm 8 cm
x xx 15 cm 15 cm 15 cm
x xx
17 m 17 m 17 m
15 15 15
11 cm 11 cm 11 cm 23 cm 23 cm 23 cm
x xx
20 m 20 m 20 m
Total Total Totalmarks marks marksachieved achieved achievedfor for forPART PART PARTBB B Chapter Chapter Chapter 2:2: Pythagoras’ 2:Pythagoras’ Pythagoras’ theorem theorem theorem
Total marks achieved for PART B Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
30 30 30 21 21 21
15
10
Book - Series I-1
r
y x
Mathletics Instant Workbooks
Copyright ©
Pythagoras’ theorem Student Book - Series I Contents Topics
Date completed
Topic 1 - Hypotenuse of the right angled triangle
__/__/__
Topic 2 - Naming the sides of a right angled triangle
__/__/__
Topic 3 - Selecting the correct Pythagoras’ rule
__/__/__
Topic 4 - Squares, square roots and Pythagorean triads
__/__/__
Topic 5 - Finding the length of the hypotenuse
__/__/__
Topic 6 - Finding the length of one of the other sides
__/__/__
Topic 7 - Miscellaneous questions on Pythagoras’ theorem
__/__/__
Topic 8 - Problem solving and Pythagoras’ theorem
__/__/__
Practice Tests Topic 1 - Topic test A
__/__/__
Topic 2 - Topic test B
__/__/__
Author of The Topics and Topic Tests: AS Kalra
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
Chapter 2 Pythagoras’ theorem
EXCEL MATHEMATICS YEAR 8
pages 124–125
Topic 1: of the rightright angled triangle UNIT 1:Hypotenuse Hypotenuse of the angled triangle Question 1 Name the hypotenuse of each right angled triangle. a
a
B
b
C
c
P
q
b
n
m
r N
R A
d
L
c
e
T
R
S
l
Q
p
M J
f
W
U V
K
L
Question 2 Name the hypotenuse of the triangle named below in the diagram. a
A
B
b P
Q
E
D
∆ADC
d
L
M
T
C
S
T
e A
P
S
Q
R
∆PST
c
J R
K
N
∆PSR
∆LJM
f D
D
B
E
H
F ∆FHG
C
∆CBD
G
Question 3 Complete the following statements. a
is the length of the side opposite to angle D.
b
is the length of the side opposite to angle E.
c
is the length of the side opposite to angle F.
d
is the length of the hypotenuse of ΔDEF.
e
is the area of the square on the side opposite to ∠D.
f
is the area of the square on the side opposite to ∠F.
12
d
E
f
F
e D
EXCEL ESSENTIAL SKILLS: YEAR 8 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
1
Pythagoras’ theorem
EXCEL MATHEMATICS YEAR 8
pages 124–125
Topic the sides of aof right angled triangle UNIT 2: 2:Naming Naming the sides a right angled triangle
For each of the following triangles, complete the table below and that the square on the hypotenuse is equal to the sum of the squares on the other two sides. 5 1 B 2 A 3 C 5
3
10 13
C
A C
4
5
16
B
A
12
B
8
20
C 24
A
8
12
A
C
10
26
9
B
15
B 20
B
9
A 34 16
25
B
C
17
15
7
C
8
6
C
A
6
12
A
4
B
15
B 30
C A
a
b
c
a2
b2
c2
a2 + b2
1 2 3 4 5 6 7 8 9 13
Chapter 2: Pythagoras’ theorem
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
2
Pythagoras’ theorem theorem Pythagoras’
EXCEL MATHEMATICS YEAR 8
page 125
Topic thethe correct Pythagoras’ rule UNIT3:3:Selecting Selecting correct Pythagoras’ rule In the following right angled triangles, circle the correct statement. 1
a a2 = b2 + c2 b b2 = a2 + c2 c c2 = a2 + b2
A
7
S
a s2 = t2 + u2 b t2 = s2 + u2 c u2 = s2 + t2
T
C B
U D
a d2 = e2 + f 2 b e2 = d2 + f 2 c f 2 = d2 + e2
2
X
8
Y
F
E
Z G
3
a x2 = y2 + z2 b y2 = x2 + z2 c z2 = x2 + y2
H
a g2 = h2 + i2 b h2 = g2 + i2 c i2 = g2 + h2
U
9
a u2 = v2 + w2 b v2 = u2 + w2 c w2 = u2 + v2
V
W
I
a j 2 = k2 + l 2 b k2 = j2 + l 2 c l2 = j2 + k2
J
4
K
5
a b2 = c2 + d2 b c2 = b2 + d2 c d2 = b2 + c2
B
C
L
D
a m2 = n2 + o2 b n2 = m2 + o2 c o2 = m2 + n2
M
10
a e2 = f 2 + g2 b f 2 = e2 + g2 c g2 = e2 + f 2
11 E
O N
F
a p2 = q2 + r2 b q2 = p2 + r2 c r2 = p2 + q2
Q
6 P
G
12
H
a h2 = i2 + j 2 b i2 = h2 + j 2 c j 2 = i2 + h2
I J
R
14
EXCEL ESSENTIAL SKILLS: YEAR 8 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
3
Pythagoras’ theorem theorem Pythagoras’
EXCEL MATHEMATICS YEAR 8
pages 35–36, 125, 128–129
UNIT 4: 4:Squares, Squares, square roots Pythagorean Topic square roots and and Pythagorean triads triads Question 1 Use your calculator to find the following squares. a 152 =
b 132 =
c 402 =
d 282 =
e 52 =
f 692 =
g 102 =
h 172 =
i 812 =
j 82 =
k 412 =
l 992 =
Question 2 Use the square root key to find n. a n2 = 169
b n2 = 841
c n2 = 576
d n2 = 4761
e n2 = 100
f n2 = 1444
g n2 = 144
h n2 = 441
i n2 = 1600
j n2 = 2809
k n2 = 784
l n2 = 5625
Question 3 Which of the following are Pythagorean triads? a {2, 4, 6}
b {9, 12, 15}
c {9, 40, 41}
d {4, 6, 10}
e {3, 4, 5}
f {8, 13, 17}
g {8, 10, 12}
h {19, 40, 41}
i {6, 8, 10}
j {5, 12, 13}
k {15, 36, 39}
l {8, 15, 17}
Question 4 Prove that the following triangles are right angled triangles. a
5
4
5
12
b
3
13
15
Chapter 2: Pythagoras’ theorem
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
4
Pythagoras’ Pythagoras’ theorem theorem
EXCEL MATHEMATICS YEAR 8
pages 125–126
UNIT 5:Finding Findingthe the length of hypotenuse the hypotenuse Topic 5: length of the
Question 1 Find the length of the hypotenuse in each of the following. (All measurements are in centimetres.) a
b
x
15
20
4
x
3
c
6
d
8
x
e
30
12
16
x
5
f
24
10
x
x
Question 2 Find the length of the hypotenuse correct to one decimal place. (All measurements are in centimetres.) a
x
x
4
4.2
e
7
x
x
d
7
3
3.5
c
5
b
5
f
1.2 3.4
x
6.5
x
3.5
16
EXCEL ESSENTIAL SKILLS: YEAR 8 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
5
Pythagoras’ Pythagoras’ theorem theorem
EXCEL MATHEMATICS YEAR 8
pages 126–127
UNIT 6:Finding Findingthe the length of one ofother the other Topic 6: length of one of the sides sides
Question 1 In the following triangles, f ind the length of the unknown sides. (All measurements are in centimetres.) a
x
12
c
x
15
12
x
d
x
f
x
41
20
6
17
e
13
b
10
x
7
40
25
Question 2 Find the length of the unknown side correct to one decimal place. (All measurements are in centimetres.) a
x
15.3
6
b
x
14
8.9
c
d
5
e
x 14.2
x
4.5
9
x
17
f
12.3
15
7
x 17
Chapter 2: Pythagoras’ theorem
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
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6
Pythagoras’ Pythagoras’ theorem theorem
EXCEL MATHEMATICS YEAR 8
UNIT 7: Miscellaneous Miscellaneous questions Pythagoras’ theorem Topic 7: questions on on Pythagoras’ theorem
pages 129–131
Question 1 In each of the following, fnd the length of the unknown sides (All measurements are in centimetres.) a
12
x
16
17
x
c
x
b
5
11
8
d
x
20
2
y
3
4
e
12
x
f
24
20
x 30
Question 2 Find the length of the unknown side correct to two decimal places. (All measurements are in centimetres.) a
b 5
x
6
3
x
12
14
c
d
7
x
6
10
x
4
e
18
x
f
5
24
x
15 21
EXCEL ESSENTIAL SKILLS: YEAR 8 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
7
Pythagoras’ Pythagoras’ theorem theorem
EXCEL MATHEMATICS YEAR 8
pages 131–132
UNIT 8:Problem Problem solving Pythagoras’ theorem Topic 8: solving andand Pythagoras’ theorem
1
Find the length of the diagonal of a square of side length 5 cm. ________________________________________
2
Find the length of the diagonal of a rectangle of length 35 cm and width 12 cm. ______________________________________________________________________________________________
3
What is the altitude of an equilateral triangle whose sides are each 16 cm long? Give your answer correct to two decimal places. __________________________________________
4
A 15 metre ladder rests against a wall and its foot is 4 metres away from the base of the wall. How high does it reach up the wall? Give your answer correct to two decimal places. ______________________________________________________________________________________________
5
The sides of a rectangle are 12 cm and 6 cm. Find the length of the diagonal. Give your answer correct to one decimal place. ______________________________________________________________________________________________
6
The hypotenuse of a right angled triangle is 30 cm. If one of the shorter sides is 18 cm, find the length of the other side. ______________________________________________________________________________________________
7
In a right angled triangle, the longest side is 39 cm and the shortest side is 15 cm. Find the length of the third side. __________________________________________________________________________________________________
8
a
Find the length of the unknown side in each of the following triangles, correct to two decimal places. (All measurements are in centimetres.) b
15
c
a
4 14
x
18
y
12
11
d
e
9
12
25
x
36
64
x
60
x 9
f
Find the perimeter of the triangle below (correct to one decimal place) by finding the hypotenuse first. 29 30
19
Chapter 2: Pythagoras’ theorem
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
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8
Pythagoras’ theorem Pythagoras’ theorem Topic TOPICTest TEST Instructions Instructions
PART PART A A
This part consists of 12 multiple-choice questions • This part consists of 12 multiple choice questions Each question is worth 1 mark • Each question is worth 1 mark Fill in only ONE CIRCLE for each question • Fill in only ONE CIRCLE for each question Calculators are NOT allowed • Calculators may be used
Time allowed: allowed: 15 15 minutes minutes Time
Total marks =Total 12 marks = 12 Marks Marks
1
A triangle is said to satisfy the rule c22 = a22 + b22 for which special triangle? acute angled right angled obtuse angled
D none of these
1
The longest side of a right angled triangle is called the shortest side middle side hypotenuse
D none of these
1
Given that c22 = a22 + b22 and a = 8, b = 15, what is the value of c? 17 23 289
D 529
1
A 2
A 3
A 4
B B
1
1
If two sides of a right angled triangle are 2.4 m and 1 m then the hypotenuse is 2.4 m 2.6 m 3.4 m
D 3.8 m
1
The Pythagorean result for a triangle ABC right angled at C is a22 = b22 + c22 b22 = a22 + c22 c22 = a22 + b22
D none of these
1
The hypotenuse of a right angled triangle is opposite to the acute angle right angle obtuse angle
D none of these
1
A 9
B obtuse angled triangles D any triangle D
A 8
The hypotenuse of a right angled triangle is 17 cm. If one side is 15 cm, the third side is 14 cm 12 cm 10 cm 8 cm
A 7
C
Pythagoras’ theorem can be applied to acute angled triangles right angled triangles
A 6
C
B
A C 5
C
B B B
B
C C
C C
If two shorter sides of a right angled triangle are 7 m and 8 m, then the hypotenuse is 65 85 113 193
A
B
C
10 In a triangle ABC right angled at C, the hypotenuse is named as
A a
B b
C c
D
1
D none of these
1
11 If two sides of a right angled triangle are 6 cm and 8 cm, then the hypotenuse is
A 10 cm
B 9.4 cm
12 If n22 = 2304 then n equals
A 38
B 42
C 12 cm
D 14 cm
1
C 48
D 52
1
Total marks achieved for PART A 20
12
TotalYEAR marks achieved forAND PART EXCEL EXCEL ESSENTIAL ESSENTIAL SKILLS: SKILLS: YEAR 88 MATHEMATICS MATHEMATICS REVISION REVISION AND EXAM EXAMA WORKBOOK WORKBOOK 11
12
Pythagoras’ theorem Mathletics Instant Workbooks – Series I
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9
Pythagoras’ Pythagoras’ theorem theorem Pythagoras’ theorem TOPIC TOPIC TOPIC TEST TEST TEST Topic Test
PART PART PARTBBBB PART
Instructions Instructions Instructions • This part consists of 15 questions This part consists of 15 questions This part consists of 15 questions Instructions • • This part consists of 15 questions
Each question is worth 2 marks Each question is worth 2 marks Each question is worth 2 marks • • • Each question is worth 1 mark Write answers in the answers-only column Write answers in the answers-only column • ••Write answers in the answers-only column Write answers in the answers-only column ••Calculators may be used Calculators may be used Calculators may be used Time allowed: •20 minutes
Total marks = 15 Total Total Totalmarks marks marks===30 30 30 Answers only Marks Marks Marks Answers Answers Answersonly only only Marks
Time Time Timeallowed: allowed: allowed:15 15 15minutes minutes minutes Questions Questions Questions Questions
111 IfIf Ifn2nn2=2 ==3844 3844 3844then then thenfind find findthe the thevalue value valueofof ofnnn
QQ Q 3636 36
222 IsIs Is{6, {6, {6,8,8, 8,10} 10} 10}a aPythagorean a Pythagorean Pythagoreantriad? triad? triad? 333 Prove Prove Provethat that thatΔPQR ΔPQR ΔPQRisisisa aright a right rightangled angled angled
111
222
111
333
111
4 7.2 cm 7.2 cm 7.2 cm 44
111
555
111
666
111
777
111
888
111
999
111
10 10 10
111
11 11 11
111
12 12 12
111
13 13 13
111
14 14 14
111
15 15 15
111
2727 27
PPP
triangle. triangle. triangle.
111
RRR
4545 45
Find Find Findthe the thelength length lengthofof ofthe the theunknown unknown unknownside side sideinin inthe the thefollowing following followingtriangles triangles trianglescorrect correct correct toto totwo two twodecimal decimal decimalplaces. places. places. 444
555 3 m 3 m 3 m
22 m 22 m 22 m
666
x xx
9.6 cm 9.6 cm 9.6 cm
x xx
777
x xx
17 m 17 m 17 m
15 m 15 m 15 m
8887 cm 7 cm 7 cm
12 m 12 m 12 m
999
1 m 1 m 1 m
x xx
24 cm 24 cm 24 cm
13 m 13 m 13 m
2 m 2 m 2 m
x xx
x xx
3 m 3 m 3 m
10 10 10
11 11 11 13 m 13 m 13 m
x xx
5 m 5 m 5 m
12 12 12 x xx
8 m 8 m 8 m
12 m 12 m 12 m
x xx
11 m 11 m 11 m
13 13 13
14 14 14
8 cm 8 cm 8 cm
x xx 15 cm 15 cm 15 cm
x xx
17 m 17 m 17 m
15 15 15
11 cm 11 cm 11 cm 23 cm 23 cm 23 cm
x xx
20 m 20 m 20 m
Total Total Totalmarks marks marksachieved achieved achievedfor for forPART PART PARTBB B Chapter Chapter Chapter 2:2: Pythagoras’ 2:Pythagoras’ Pythagoras’ theorem theorem theorem
Total marks achieved for PART B Pythagoras’ theorem Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
30 30 30 21 21 21
15
10
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