year 8 maths

376 Chapter 6 Angle relationships and properties of geometrical figures 1
7 Use your algebra skills to find the value of x in these diagrams.
a
b
95°
c
(4x)° (3x)°
95°
(5x)°
(2x)°
x°
x°
(2x)°
85°
8 The word ‘bisect’ means to cut in half.
a Which quadrilaterals have diagonals that bisect each other?
b Which quadrilaterals have diagonals that bisect all their interior angles?
9 By considering the properties of special quadrilaterals, decide if the following are always true.
a A square is a type of rectangle.
b A rectangle is a type of square.
c A square is a type of rhombus.
d A rectangle is a type of parallelogram.
e A parallelogram is a type of square.
f A rhombus is a type of parallelogram.
10 Is it possible to draw a non-convex quadrilateral with two or more interior reflex angles? Explain
and illustrate.
ENRICHMENT
– –
11
Proof
11 Complete these proofs of two different angle properties of quadrilaterals.
a Angle sum = a + b + c + + +
= + (angle sum of a triangle)
=
b°
a° f °
c°
d°
e°
b ∠ ADC + + + = 360° (angle sum
of a quadrilateral)
Reflex ∠ ADC = 360 − ∠ ADC
= 360 − (360 − ( + + ))
= + +
A
D
a°
b°
B
c° C
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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