The Theorem of Pythagoras (Grade 8) — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 8 · Pythagoras

The Theorem of Pythagoras (Grade 8)

EXAM-STYLE CLASS TEST

Marks

Duration

45 minutes

Questions

Name:

Class:

Date:

Mark

/ 28

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 longest side is called the …
(1)
A)base
B)hypotenuse
C)height
D)perpendicular
1.2
A right-angled triangle has legs of 9 cm and 12 cm. Its hypotenuse is …
(1)
A)21 cm
B)15 cm
C)225 cm
D)10,5 cm
1.3
A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. The other leg is …
(1)
A)18 cm
B)12 cm
C)8 cm
D)194 cm
1.4
Which set of lengths forms a right-angled triangle?
(1)
A)4 ; 5 ; 6
B)8 ; 15 ; 17
C)5 ; 6 ; 7
D)3 ; 4 ; 6
1.5
To find a SHORTER side of a right-angled triangle you …
(1)
A)add the squares
B)SUBTRACT the squares
C)add the sides
D)subtract the sides
1.6
A ladder 10 m long leans against a wall with its foot 6 m from the wall. It reaches … up the wall.
(1)
A)4 m
B)8 m
C)16 m
D)11,66 m
1.7
The theorem of Pythagoras applies ONLY to …
(1)
A)all triangles
B)right-angled triangles
C)isosceles triangles
D)equilateral triangles
1.8
A rectangle is 8 cm by 15 cm. Its DIAGONAL is …
(1)
A)23 cm
B)17 cm
C)120 cm
D)11,5 cm
1.9
In △ABC, AB = 6, BC = 8 and AC = 10. The right angle is at …
(1)
A)A
B)B
C)C
D)there is none
1.10
For the 9-12-15 triangle, the AREA is …
(1)
A)108 cm²
B)54 cm²
C)67,5 cm²
D)36 cm²

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 right-angled triangle below, two sides are given.

2.1
Write down the theorem of Pythagoras for this triangle, and explain what each of the squares in the statement represents.
(3)
2.2
Hence calculate x.
(3)
2.3
Explain how you know x must be the longest side, and hence calculate the perimeter and the area of the triangle.
(4)

Question 3

[8 MARKS]

A triangle has sides of 8 cm, 15 cm and 17 cm.

3.1
Show, by calculation, whether this triangle is right-angled.
(4)
3.2
Where in the triangle is the right angle? Give a reason, calculate the area of the triangle, and then show that a triangle with sides 8 cm, 15 cm and 18 cm is NOT right-angled.
(4)

TOTAL: 28 marks

This question paper consists of 3 questions.

Statement	Reason

Statement	Reason