year 8 maths

176 Chapter 3 Measurement and Pythagoras’ theorem
Example 24
11 If a 2 + b 2 = c 2 , we know that the triangle must have a right angle. Which of these triangles must
have a right angle?
a 12
b 1
c 3
9
15
2
1
2
5
d
15
17
8
e
8
6
5
f
41
40
9
12 If a 2 + b 2 = c 2 is true, complete these statements.
a c 2 − b 2 = ___ b c 2 − a 2 = ___ c c = _______
13 This triangle is isosceles. Write Pythagoras’ theorem using the given letters. Simplify if possible.
c
x
ENRICHMENT
– –
14
Pythagoras’ theorem proof
14 There are many ways to prove Pythagoras’ theorem, both algebraically and geometrically.
a Here is an incomplete proof of the theorem that uses this illustrated geometric construction.
Area of inside square = c 2
a
b
Area of 4 outside triangles = 4 × 1 × base × height
2
= _______
Total area of outside square = (_____ + _____) 2
= a 2 + 2ab + b 2
Area of inside square = Area outside square − Area of 4 triangles
= _______ − _______
= _______
Comparing results from the first and last steps gives:
c 2 = _______
b
a
c
b
c
c
c
a
a
b
b Use the internet to search for other proofs of Pythagoras’ theorem. See if you can explain and
illustrate them.
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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