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Deductive geometry Test B
Name: ___________________________
Section A Multiple Choice
1
The value of the pronumeral a in the
pair of similar triangles in the figure
below is:
A
B
C
D
2
B
C
D
3
3
4
1
9
7
28
2
34
7
The values of the pronumerals d and e,
respectively, in following pair of
congruent triangles are:
A
15
The values of the pronumerals b and c,
respectively, in the figure below are:
A
C
A
B
C
D
B
The test you could use to prove that
TRS  SUT is:
A
B
C
D
10, 12
2
1
6 and 22
3
2
2
16 and 24
3
2
1
14 and 22
5
2
Maths Quest 10 for New South Wales 5.3 pathway
4
Chapter 5
21 and 25
21 and 29
25 and 29
25 and 21
C
SAS
AAS
RHS
SSS
1
5
Which of the following triangles would
be congruent to ABC?
B
8
Which of the following statements is
not true?
A a square is a trapezium
B a rhombus is a parallelogram
C a rectangle is a square
D a parallelogram is a trapezium
C
9
Which of the following properties is
true for a rectangle?
A diagonals bisect the angles they
pass through
B all sides are equal
C diagonals are perpendicular
D diagonals are equal
D
10
A quadrilateral is a rhombus if:
A all sides are equal
B opposite angles are supplementary
C diagonals are equal in length
D all angles are equal
A
11
If a quadrilateral has one pair of
opposite sides parallel and equal, then
the quadrilateral must be a:
A trapezium
B parallelogram
C square
D rhombus
B
A
B
C
D
6
A quadrilateral with both pairs of
opposite sides parallel is:
A a parallelogram
B a trapezium
C a square
D a rectangle
A
7
A square is:
A a parallelogram with two adjacent
sides equal
B a quadrilateral with opposite sides
parallel
C a parallelogram with two adjacent
sides equal
D a rectangle with two adjacent sides
equal
D
Maths Quest 10 for New South Wales 5.3 pathway
Chapter 5
2
Deductive geometry Test B
Name: ___________________________
Section B Short/Extended answer
1
Find the value of the pronumeral f’ in the pair
of similar triangles.
f 30

7 16
30
f 
7
16
1
f  13
8
2
2
Find the value of the pronumerals g and h in
the figure below.
g  12 12

20
16
12
g  12   20
16
g  12  15
g  15  12
g 3
h
8

20 16
8
h   20
16
h  10
2
3
In the figure below show that PQR  RST.
PQR = RST (alternate angles on parallel
lines)
QPR = RTS (alternate angles on parallel
lines)
SR = RQ (given)
PQR  RST (ASA)
3
Maths Quest 10 for New South Wales 5.3 pathway
Chapter 5
3
4
Use congruence to prove that
ABE  DEB
5
True or false?
(a) A rhombus is a parallelogram.
(b) A parallelogram is a rhombus.
AB = DE (given)
ABE = DEB = 90 (given)
BE is common.
 ABE  DEB (SAS or RHS)
 BAE = EDB (Corresponding angles in
congruent triangles are
equal.)
3
2
(a) true
(b) false
6
Prove that ABCD is a parallelogram by
showing opposite angles are equal.
ABC = ADC (given)
DAB = 60 (co-interior angles equal as
ABCD)
BCD = 60 (co-interior angles equal as
ABCD)
 DAB = BCD
 Opposite angles are equal
 ABCD is a parallelogram.
3
7
Name any quadrilaterals that have at least one
pair of sides equal and parallel.
Parallelogram, rhombus, rectangle and square.
2
8
In the figure below show that ABC  ADC.
AC is a common side
ACB = ACD (given as 90o)
BC = CD (given)
ABC  ADC (SAS)
3
Maths Quest 10 for New South Wales 5.3 pathway
Chapter 5
4
PQR = PSR (given)
QPR = SRP (given) = 40
PR is common
 PQR  PSR (AAS)
 PQ = PS and QR = SR
Also PQR is isosceles, since
QPR = QRP = 40 (angle sum of a triangle
is 180)
 PQ = QR
 All sides are equal
 PQRS is a rhombus
9
Prove that PQRS is a rhombus
10
What am I? I have four sides, four corners and
four angles. My sides can be the same length
but don’t need to be. My angles can also all be
different. I always have at least one pair of
parallel sides. I am………..
How many triangles can you see?
11
12
4
2
1
Draw three company logo’s which have
quadrilaterals in them.
Maths Quest 10 for New South Wales 5.3 pathway
Chapter 5
5