year 8 maths

8H
Using congruent triangles to establish properties of quadrilaterals
511
15 A trapezium, ABCD, has one pair of parallel sides.
a Which angle is equal to ∠BAE ?
b Which angle is equal to ∠ABE ?
c Explain why △ ABE is not congruent to △CDE .
A
D
E
C
B
16 Use the information given for this kite to give reasons for the
following properties. You may assume that ∠ADE =∠CDE ,
as marked.
a ∠DAE =∠DCE
b △ AED ≡ △CED
c ∠AED =∠CED = 90°
A
D
E
C
B
ENRICHMENT
– –
17
Prove the converse
17 Prove the following results, which are the converse (reverse) of some of the proofs completed
earlier in this exercise.
a If the opposite sides of a quadrilateral are equal, then the quadrilateral is a parallelogram; that is,
show that the quadrilateral has two pairs of parallel sides.
D
C
E
A B
b If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
D
E
C
A
B
c
If the diagonals of a parallelogram are equal, then the parallelogram is a rectangle.
D
C
A AC = BD B
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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