year 8 maths

8G
Similar triangles
501
• The hypotenuse and a second side of a right-angled triangle are proportional to the
hypotenuse and second side of another right-angled triangle.
B
A
4 m
5 m
C
F
12 m
15 m
E
DF
AC = EF
BC = 3
Scale factor
Key ideas
■ If two triangles △ABC and △DEF are similar, we write △ABC ||| △DEF .
■ Abbreviations such as AAA are generally not used for similarity in NSW.
D
Example 11
Deciding if two triangles are similar
Decide, with reasons, why these pairs of triangles are similar.
a
C
F
b
C
E
75° 70°
D
5 cm
A
50°
2 cm
B
E
10 cm
50°
4 cm
D
A
70°
75°
B
F
SOLUTION
ED
a
AB = 4 2 = 2
∠B =∠E = 50°
EF
BC = 10 5 = 2
∴ △ABC is similar to △DEF, using SAS.
b ∠A =∠D
∠B =∠E
∴ △ABC is similar to △DEF, using AAA .
EXPLANATION
Work out the ratio of the two pairs of corresponding
sides to see if they are equal. Note that the angle
given is the included angle between the two given
pairs of corresponding sides.
Two pairs of equal angles are given. This implies
that the third pair of angles are also equal and that
the triangles are similar.
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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