year 8 maths

6C
Triangles
369
11 A triangle is constructed using two radii and a chord.
O
A
B
a What type of triangle is △ AOB ? Explain.
b Name two angles that are equal.
c Find ∠ ABO if ∠BAO is 30° .
d Find ∠ AOB if ∠OAB is 36° .
e Find ∠ ABO if ∠ AOB is 100° .
12 To prove that the angle sum of a triangle is 180° , work through these steps with the given diagram.
D
B
b°
E
A
a°
c°
C
a Using the pronumerals a, b or c , give the value of these angles and state a reason.
i ∠ ABD ii ∠CBE
b What is true about the three angles ∠ ABD , ∠ ABC and ∠CBE and why?
c What do parts a and b above say about the pronumerals a, b and c , and what does this say about
the angle sum of the triangle ABC ?
13 Prove that a triangle cannot have two right angles.
14 Prove that an equilateral triangle must have 60° angles.
15 A different way of proving the angle sum of a triangle is to use this diagram.
B
b°
D
A
a°
c°
C
a Give a reason why ∠BCD = b .
b What do you know about the two angles ∠BAC and ∠ ACD and why?
c What do parts a and b above say about the pronumerals a, b and c , and what does this say about
the triangle ABC ?
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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