Pythagoras' Theorem: Finding the Missing Side — Worksheet & Memo

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Grade 9 · Geometry

Pythagoras' Theorem: Finding the Missing Side

EXAM-STYLE CLASS TEST

Marks

Duration

1 hour

Questions

Name:

Class:

Date:

Mark

/ 39

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
In a right-angled triangle, the square on the hypotenuse equals …
(1)
A)the sum of the other two sides
B)the SUM of the squares on the other two sides
C)the difference of the other two squares
D)twice the area
1.2
A right-angled triangle has legs of 8 cm and 15 cm. Its hypotenuse is …
(1)
A)23 cm
B)17 cm
C)289 cm
D)12 cm
1.3
A ladder 25 m long has its foot 7 m from a wall. It reaches … up the wall.
(1)
A)18 m
B)24 m
C)26 m
D)32 m
1.4
Which set of lengths does NOT form a right-angled triangle?
(1)
A)5 ; 12 ; 13
B)9 ; 12 ; 15
C)6 ; 8 ; 10
D)4 ; 5 ; 6
1.5
In △PQR, PQ = 9, QR = 12 and PR = 15. The right angle is at …
(1)
A)P
B)Q
C)R
D)there is none
1.6
To find a SHORTER side of a right-angled triangle, you …
(1)
A)add the two squares
B)SUBTRACT the squares
C)add the two sides
D)halve the hypotenuse
1.7
A rectangle is 24 cm by 7 cm. Its DIAGONAL is …
(1)
A)31 cm
B)25 cm
C)168 cm
D)17 cm
1.8
A right-angled triangle has legs of 5 cm and 5 cm. Its hypotenuse, in surd form, is …
(1)
A)10 cm
B)50 cm
C)25 cm
D)25 cm
1.9
The theorem of Pythagoras can be used to check whether a triangle …
(1)
A)is isosceles
B)is RIGHT-ANGLED
C)is equilateral
D)has equal angles
1.10
A pole 12 m tall is supported by a wire from its top to a point 5 m from its base. The wire is …
(1)
A)17 m
B)13 m
C)7 m
D)60 m

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[10 MARKS]

In the diagram below, △PQR has Q̂ = 90°, PQ = 8 cm and QR = 15 cm. S is a point on QR such that QS = 5 cm. The diagram is not drawn to scale.

2.1
Calculate the length of PR. Give a reason for your statement.
(3)
2.2
Calculate the length of PS, correct to two decimal places.
(3)
2.3
Hence calculate the perimeter of △PSR, correct to one decimal place.
(4)

Question 3

[10 MARKS]

In the diagram below, ABCD is a quadrilateral with AB = 9 cm, BC = 12 cm, AC = 15 cm, CD = 8 cm and AD = 17 cm. The diagram is not drawn to scale.

3.1
Show, by calculation, that AB̂C = 90°.
(3)
3.2
Show that △ACD is right-angled and write down which angle is the right angle.
(4)
3.3
Hence calculate the area of quadrilateral ABCD.
(3)

Question 4

[9 MARKS]

The diagram below shows a closed rectangular box with a length of 12 cm, a breadth of 9 cm and a height of 8 cm. AC is a diagonal of the base and AG is the longest straight rod that will fit inside the box.

4.1
Calculate the length of the base diagonal AC.
(3)
4.2
Hence calculate the length of AG.
(3)
4.3
A straight metal rod is 16 cm long. Will it fit inside the closed box? Give a reason for your answer.
(3)

TOTAL: 39 marks

This question paper consists of 4 questions.

Statement	Reason

Statement	Reason

Statement	Reason

Statement	Reason