year 8 maths

486 Chapter 8 Transformations and congruence
8E Congruent triangles
Imagine the sorts of design and engineering problems we would face if we could not guarantee that two
objects, such as window panes or roof truss frames, were not the same size or shape. Furthermore, it
might not be possible or practical to measure every length and angle to test for congruence. In the case of
triangles, it is possible to consider only a number of pairs of sides or angles to test whether or not they are
congruent.
Let’s start: How much information is enough?
When given one corresponding angle (say 30° ) and one corresponding equal side length (say 3 cm ), it is
clearly not enough information to say two triangles are congruent. This is because more than one triangle
can be drawn with the given information.
30°
3 cm
30°
3 cm
30°
3 cm
Decide if the following information is enough to determine if two triangles are congruent. If you can
draw two non-identical triangles, then there is not enough information. If you can draw only one unique
triangle, then you have the conditions for congruence.
• △ ABC with AC = 4 cm and ∠C = 40°
• △ ABC with AB = 5 cm and AC = 4 cm
• △ ABC with AB = 5 cm, AC = 4 cm and ∠A = 45°
• △ ABC with AB = 5 cm, AC = 4 cm and BC = 3 cm
• △ ABC with AB = 4 cm, ∠ A = 40° and ∠B = 60°
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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