year 8 maths

8E
Congruent triangles
491
8 Two adjoining triangular areas of land have the dimensions shown. Use Pythagoras’ theorem to
help decide if the two areas of land are congruent.
5 km
12 km
13 km
5 km
9 a Explain why SSA is not sufficient to prove that two triangles are congruent. Draw diagrams to
show your reasoning.
b Explain why AAA is not sufficient to prove that two triangles are congruent. Draw diagrams to
show your reasoning.
10 Here is a suggested proof showing that the two triangles in this diagram are congruent.
A
B
C
D
E
In △ ABC and △EDC :
∠CAB =∠CED (alternate angles in parallel lines)
∠ ACB =∠ECD (vertically opposite angles)
AC = EC (given equal and corresponding sides)
∴ △ ABC ≡ △EDC (AAS)
Write a proof (similar to the above) for these pairs of congruent triangles. Any of the four tests
(SSS, SAS, AAS or RHS) may be used.
a A B
C
b
D
D
E
A
B
C
c
A B d
B
D
C
A
C
D
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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