year 8 maths

364 Chapter 6 Angle relationships and properties of geometrical figures 1
6C Triangles
A triangle is a polygon with three sides. As a real-life object, the triangle is a very rigid shape and this
leads to its use in the construction of houses and bridges. It is one of the most commonly used shapes in
design and construction.
Knowing the properties of triangles can help to solve many geometrical problems, and this knowledge can
be extended to explore other more complex shapes.
Let’s start: Illustrating the angle sum and the triangle inequality
You can complete this task using a pencil and ruler or using dynamic
geometry software.
• Draw any triangle and measure each interior angle and each side.
• Add all three angles to find the angle sum of your triangle.
• Compare your angle sum with the results of others. What do
you notice?
• Add the two shorter sides together and compare that sum to the longest side.
• Is the longest side opposite the largest angle?
If dynamic geometry is used, drag one of the vertices to alter the sides and the interior angles.
Now check to see if your conclusions remain the same.
Key ideas
■ A triangle has:
• 3 sides: AB, AC, BC
• 3 vertices (the plural of ‘vertex’): A, B, C
• 3 interior angles: ∠ABC, ∠BAC, ∠ACB
A
∠BAC
C
B
vertex
side
■ Triangles classified by side lengths
• Sides with the same number of dashes are of equal length.
Scalene
Isosceles
apex
Equilateral
60°
base
angles
60°
60°
base
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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