pyth-thm-workbook

Pythagoras’ Theorem n t  S t ude

Book  - Ser i  ie    s e   I 1

r 

y x

Mathlecs Instant Workbooks

Copyright ©

Pythagoras’ theorem Student Book - Series I Contents Topics

Date completed

Topic 1 - Hypotenuse of the right angled triangle 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 Pythagorean triads

 __/__/__ 

Topic 5 - Finding the length of the hypotenuse

 __/__/__ 

Topic 6 - Finding the length of one of the other sides

 __/__/__ 

Topic 7 - Miscellaneou Miscellaneouss 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 es I

Copyright © 3P Learning

Pythagoras’ theorem Topic 1: Hypotenuse of the right angled triangle QUESTION 1 a

Name the hypotenuse of each right angled triangle. a

B

b

C

L

c

P

n

m c

q

b

r N

R  A

l M

T

d

Q

 p

R

J

W

e

f 

U

S

V

QUESTION 2 a

B

b

P

Q

E

D

C

d

L

M

J

S

R

K

N

∆PSR

T

P

S

Q

R ∆PST

c

T

∆ ADC

a

L

Name the hypotenuse of the triangle named below in the diagram.

 A

QUESTION 3

K

∆LJM

e  A

f  D

E

H F

D

B

∆FHG

C

∆CBD

G

Complete the following statements. 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 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.

Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

d 

E

F

e  f  D

1

Pythagoras’ theorem Topic 2: Naming the sides of 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. 1

2

B

5

 A

3

C

B

5

3

10 6 13

C

12

 A

4

 A

B

C

4

5

16

C

6

 A

12

B

C

8

12

8

9

17

20 C

 A

 A

B

15

15 B C

7 24

8

9

20

B

 A

C

10

34 16

 A

25

B

26

15

B 30 C

 A

a

b

c

a2

b2

c 2

a2 + b2

1 2 3 4 5 6 7 8 9

Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

2

Pythagoras’ theorem Topic 3: Selecting the correct Pythagoras’ rule In the following right angled triangles, circle the correct statement. 1

a

 A

b c

a2 = b2 + c2 b2 = a2 + c2 c2 = a2 + b2

7

S

a

T

b c

s2 = t 2 + u2 t 2 = s2 + u2 u2 = s2 + t 2

C B

U D

a

2

b c

d 2 = e2 + f 2 e2 = d 2 + f 2  f 2 = d 2 + e2

X

8

Y

a b c

 x2 = y2 + z2  y2 = x2 + z2  z2 = x2 + y2

F

E

Z G

3

U

H

a b c

g2 = h2 + i2 h2 = g2 + i2 i2 = g2 + h2

a

9

b c V

u2 = v2 + w2 v2 = u2 + w2 w2 = u2 + v2

W

I J

4

a b c

 j 2 = k 2 + l 2 k 2 = j 2 + l 2 l2 = j 2 + k 2

K

10

a

B

b c C

L

5

b2 = c2 + d 2 c2 = b2 + d 2 d 2 = b2 + c2

D

a

M

b c

m2 = n2 + o2 n2 = m2 + o2 o2 = m2 + n2

11

a

E

b c

e2 = f 2 + g2  f 2 = e2 + g2 g2 = e2 + f 2

O N

F

Q

6

a b

P

c

 p2 = q2 + r2 q2 = p2 + r2 r2 = p2 + q2

G

a

12 H

b c

h2 = i2 + j 2 i2 = h2 + j 2  j 2 = i2 + h2

I J R

Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

3

Pythagoras’ theorem Topic 4: Squares, square roots and Pythagorean triads QUESTION 1

a

Use your calculator to find the following squares. b 132 =

c 402 =

d 282 =

e 52 =

f  692 =

g

102 =

h 172 =

i 812 =

 j

82 =

k 412 =

l 992 =

152 =

QUESTION 2

Use the square root key to find n.

a

n

2

b

n

2

c

n

2

d

n

2

e

n

2

f 

n

2

g

n

2

h

n

2

i

n

2

n

2

k

n

2

l

n

2

 j

 = 169  = 4761  = 144  = 2809

QUESTION 3

a

 = 841  = 100  = 441  = 784

 = 576  = 1444  = 1600  = 5625

Which of the following are Pythagorean triads? 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}

{2, 4, 6}

QUESTION 4

Prove that the following triangles are right angled triangles.

a 5

4 5

12

b 3

Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

13

4

Pythagoras’ theorem Topic 5: Finding the length of the hypotenuse QUESTION 1

Find the length of the hypotenuse in each of the following. (All measurements are in centimetres.)

a

b

15

20

4

 x 

 x 

3

c

12

d 6

8

5

 x 

 x 

e

24

f  30

16 10  x   x 

QUESTION 2

Find the length of the hypotenuse correct to one decimal place. (All measurements are in centimetres.) 5

5

a

b 3  x 

 x 

3.5

c

d

7

7

 x 

 x 

4

4.2

e

f  1.2

6.5 3.4  x 

 x 

3.5

Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

5

Pythagoras’ theorem Topic 6: Finding the length of one of the other sides QUESTION 1

In the following triangles, triang les, f ind the length of o f the unknown sides. (All measurements mea surements are in centimetres.)

a

 x 

b 20

12

12

13  x 

c

d 15

6

 x 

 x 

10 17

e

 x 

41

f  7

x 

40

QUESTION 2

25

Find the length of the unknown side correct to one decimal place. (All measurements are in centimetres.) 6

a

b  x 

15.3 14

 x 

8.9

c

d

5

9  x 

 x 

17

14.2

e

f   x 

4.5

15

12.3

7

 x 

Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

6

Pythagoras’ theorem Topic 7: Miscellaneous questions on Pythagoras’ theorem QUESTION 1

In each of the following, fnd the length of the unknown sides (All measurements are in centimetres.)

a

b

5

 x

12 17

11

 x 8

c

16

x

d  x 2

20

 y 3 4

e

f  12

24

 x

 x 30

20

QUESTION 2

Find the length of the unknown side correct to two decimal places. (All measurements are in centimetres.)

a

b

3

 x

5

 x

6

12

14

c

d 6 7

10

x

 x

4

e

 x

f  5 24

15 21

 x

Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

7

Pythagoras’ theorem Topic 8: Problem solving and 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. 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, nd 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

Find the length of the unknown side in each of the following triangles, correct to two decimal places. (All measurements are in centimetres.)

a

b

c

a

4 14

15

 x 18

12

 y

11

d

e 9

f 

12

36 64

25

 x

9

 x

60

 x

Find the perimeter of the triangle below (correct to one decimal place) by nding the hypotenuse rst. 29

30

Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

8

Pythagoras’ theorem Topic Test Instructions

PART A This part consists of 12 multiple-choice questions Each question is worth 1 mark Fill in only ONE CIRCLE for each question Calculators are NOT allowed

Time allowed: 15 minutes

Total marks = 12 Marks

1

2

3

4

A triangle is said to satisfy the rule c2 = a2 + b2 for which special triangle? A acute angled B right angled C obtuse angled

D

none of these

1

The longest side of a right angled triangle is called the A shortest side B middle side C hypotenuse

D

none of these

1

Given that c2 = a2 + b2 and a = 8, b = 15, what is the value of c? A 17 B 23 C 289

D

529

1

Pythagoras’ theorem can be applied to A acute angled triangles

C 5

6

7

8

9

12

any triangle

1

1

If two sides of a right angled triangle are 2.4 m and 1 m then the hypotenuse is A 2.4 m B 2.6 m C 3.4 m

D

3.8 m

1

The Pythagorean result for a triangle ABC right angled at C is 2 2 2 2 2 2 2 2 2 A a  = b  + c B b  = a  + c C c  = a  + b

D

none of these

1

The hypotenuse of a right angled triangle is opposite to the A acute angle B right angle C obtuse angle

D

none of these

1

If two shorter sides of a right angled triangle are 7 m and 8 m, then the hypotenuse is 65

B

85

C

113

D

193

1

In a triangle ABC right angled at C, the hypotenuse is named as

A 11

obtuse angled triangles

The hypotenuse of a right angled triangle is 17 cm. If one side is 15 cm, the third side is A 14 cm B 12 cm C 10 cm D 8 cm

A 10

right angled triangles

B D

a

B

b

C

D

c

none of these

1

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 C 12 cm D 14 cm

1

If n2 = 2304 then n equals A 38 B 42

1

C

48

D

52

Total marks achieved for PART A Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

12

9

Pythagoras’ theorem Topic Test Instructions

PART B This part consists of 15 questions Each question is worth 1 mark Write answers in the answers-only column

Time allowed: 20 minutes

Total marks = 15

Questions 1

If n2 = 3844 then nd the value of n

2

Is {6, 8, 10} a Pythagorean triad?

3

Answers only Q 36

Prove that ΔPQR is a right angled triangle.

Marks

1

1

2

1

3

1

4

1

5

1

6

1

7

1

8

1

9

1

10

1

11

1

12

1

13

1

14

1

15

1

27

P

R

45

Find the length of the unknown side in the following triangles correct to two decimal places. 4

5

7.2 cm

17 m

 x 

3m

22 m

6  x 

9.6 cm 15 m

 x 

7

8 12 m

9

7 cm

1m 24 cm

 x 

13 m

2m

 x 

 x 

3m

10

11 13 m

5m

12

8m

 x 

 x 

12 m

 x 

11 m

13

14

15

8 cm

11 cm

 x 

23 cm

17 m  x 

15 cm

 x 

20 m

Total marks achieved for PART B Pythagoras’ Pythagora s’ theorem Mathletics Instant Workbooks – Series I

Copyright © 3P Learning

15

10