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 verify 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
• Thispartconsistsof12multiplechoicequestions
Each question is worth 1 mark
• Eachquestionisworth1mark
Fill in only ONE CIRCLE for each question
• FillinonlyONECIRCLEforeachquestion
Calculators are NOT allowed
• Calculatorsmaybeused
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
Aa
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
A10 cm
B 9.4 cm
12 If n22 = 2304 then n equals
A38
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
•
Thispartconsistsof15questions
Thispartconsistsof15questions
Thispartconsistsof15questions
Instructions ••
This part consists of 15 questions
Eachquestionisworth2marks
Eachquestionisworth2marks
Eachquestionisworth2marks
•••
Each question is worth 1 mark
Writeanswersintheanswers-onlycolumn
Writeanswersintheanswers-onlycolumn
•••Writeanswersintheanswers-onlycolumn
Write answers in the answers-only column
••Calculatorsmaybeused
Calculatorsmaybeused
Calculatorsmaybeused
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
7.2cm
7.2cm
7.2cm 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
3m
3m
3m
22m
22m
22m
666
x xx
9.6cm
9.6cm
9.6cm
x xx
777
x xx
17m
17m
17m
15m
15m
15m
8887cm
7cm
7cm
12m
12m
12m
999
1m
1m
1m
x xx
24cm
24cm
24cm
13m
13m
13m
2m
2m
2m
x xx
x xx
3m
3m
3m
10
10
10
11
11
11
13m
13m
13m
x xx
5m
5m
5m
12
12
12
x xx
8m
8m
8m
12m
12m
12m
x xx
11m
11m
11m
13
13
13
14
14
14
8cm
8cm
8cm
x xx
15cm
15cm
15cm
x xx
17m
17m
17m
15
15
15
11cm
11cm
11cm
23cm
23cm
23cm
x xx
20m
20m
20m
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