year 8 maths

646
3 a yes, 2 b yes, 2 c yes, 4 d yes, 4
4 a i (AB, EF ), (BC, FG), (CD, GH), (DA, HE )
ii (∠A, ∠E ), (∠B, ∠F), (∠C, ∠G), (∠D, ∠H )
iii 2 iv a = 100, x = 2, y = 3
b i (AB, DE), (BC, EF), (CA, FD)
ii (∠A, ∠D), (∠B, ∠E), (∠C, ∠F)
iii 1 iv x = 3
3
c i (AB, EF), (BC, FG), (CD, GH), (DA, HE)
ii (∠A, ∠E), (∠B, ∠F), (∠C, ∠G), (∠D, ∠H)
iii 1.5 iv a = 40, x = 4, y = 4.5
d i (AB, FG), (BC, GH), (CD, HI), (DE, IJ), (EA, JF)
ii (∠A, ∠F), (∠B, ∠G), (∠C, ∠H), (∠D, ∠I), (∠E, ∠J)
iii 2.5 iv a = 115, x = 5
5 a Yes, all ratios are 2.
b Yes, squares of different sizes.
c No, ratios are not equal.
d Yes, ratios are both 0.4 with equal angles.
6 360 cm
7 15 cm
8 1.25
9 3
10 a True, angles and side ratios will be equal.
b False, side ratios may be different.
c True, angles and side ratios will be equal.
d False, angles and side ratios may be different.
e False, angles may be different.
f False, side ratios and angles may be different.
g False, side ratios and angles may be different.
h False, side ratios and angles may be different.
i True, shape is always the same.
11 a no b No, they can have different shapes.
12 1 : 16
13 a i √8 ii 2
2
b = √2 (small to big)
√2
c Using Pythagoras’ theorem, the side length of the 2nd
2 2
x x x
square is √( + = 2
2) ( √
2) 2 = x
√2 .
So the scale factor is x ÷ x
√2 = x × √2
x = √2.
d 2 (small to big)
Exercise 8G
1 a △ ABC ||| △ EFD
b △ ABC ||| △ FDE
c △ ABC ||| △ DEF
d △ ABC ||| △ DEF (order does not matter)
2 a Two angles of △ ABC are equal to two angle of △ EFD.
b Two sides are proportional and the included angles are
equal.
c The hypotenuses are proportional and so is another pair
of sides.
d Three sides of △ ABC are proportional to three sides of
△ DEF.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
3 a DE
AB = 10
5 = 2
DF
AC = 24
12 = 2
EF
BC = 26
13 = 2
∴ △ ABC ||| △ DEF
b ∠A = ∠D
∠B = ∠E
∴ △ ABC ||| △ DEF
c DE
AB = 10
5 = 2
∠D = ∠A
DF
AC = 6 3 = 2
∴ △ ABC ||| △ DEF
d ∠D = ∠A = 90°
EF
BC = 26
13 = 2
DF
AC = 22
11 = 2
∴ △ ABC ||| △ DEF
e ∠E = ∠B = 90°
DF
AC = 4 1 = 4
EF
BC = 2
0.5 = 4
∴ △ ABC ||| △ DEF
DE
f
AB = 9 6 = 1.5
∠D = ∠A
DF
AC = 18
12 = 1.5
∴ △ ABC ||| △ DEF
g ∠A = ∠D
∠C = ∠F
∴ △ ABC ||| △ DEF
h DE
AB = 10
4 = 2.5
DF
AC = 15
6 = 2.5
EF
BC = 15
6 = 2.5
∴ △ ABC ||| △ DEF
4 a x = 8, y = 10 b x = 12, y = 6
c x = 15, y = 4 d x = 3, y = 15
5 a 2.5
b yes (three pairs of sides are propotional)
c 2.5
6 a yes b no c no d yes
7 4 m
8 a yes b 2.5 c 15 m
9 If two angles are known, then the third is automatically
known using the angle sum of a triangle.
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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