year 8 maths

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Introducing Pythagoras’ theorem
175
6 Complete this table and answer the questions.
a b c a 2 b 2 a 2 + b 2 c 2
3 4 5
6 8 10
8 15 17
a Which two columns give equal results?
b What would be the value of c 2 if:
i a 2 = 4 and b 2 = 9 ? ii a 2 = 7 and b 2 = 13 ?
c What would be the value of a 2 + b 2 if:
i c 2 = 25 ? ii c 2 = 110 ?
7 Check that a 2 + b 2 = c 2 for all these right-angled triangles.
a 4
b 8
c
15
5
3
15
17
9 12
d
5
13
12
e
40 f
41
9
6
6.5
2.5
PROBLEM-SOLVING AND REASONING
8, 9, 11 8, 9, 11, 12
9–13
8 Write down Pythagoras’ theorem using the letters given these diagrams.
a
b
c
x
a
b
b
a
d
x
d
h
9 A cable connects the top of a 30 m mast to a point on the ground. The cable is 40 m long and
connects to a point 20 m from the base of the mast.
a Using c = 40 , decide if a 2 + b 2 = c 2 .
b Do you think the triangle formed by the mast and the cable is right angled? Give a reason.
10 (3, 4, 5) and (5, 12, 13) are Pythagorean triads since 3 2 + 4 2 = 5 2 and 5 2 + 12 2 = 13 2 .
Find 10 more Pythagorean triads, using whole numbers less than 100 .
Extension: Find the total number of Pythagorean triads with whole numbers of less than 100 .
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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