year 8 maths

370 Chapter 6 Angle relationships and properties of geometrical figures 1
ENRICHMENT
– –
16
Angle in a semicircle
16 The angle sum of a triangle can be used to prove other theorems, one of
which relates to the angle in a semicircle. This theorem says that ∠ ACB in
a semicircle is always 90°, where AB is a diameter.
C
C
B
A
C
a Use your knowledge of isosceles triangles to find the value of a, b
and c in this circle.
b What do you notice about the sum of a and c ?
30°
a° c° b°
c
Repeat parts a and b above for this circle.
a° c° b°
60°
d Repeat parts a and b above for this circle.
c°
a°
b°
16°
e
f
What do you notice about the sum of a and c for all the circles above?
Prove this result generally by finding:
i a, b and c in terms of x
ii the value of a + c
a°
c°
b°
x°
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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