Download chap05-test

Deductive geometry Test A
Name: ___________________________
Section A Multiple Choice
1
2
The value of the pronumeral a in the
pair of similar triangles in the figure
below is:
A
2
B
3
C
3
D
6
C
3
A
B
C
D
1
8
1
4
The value of the pronumeral b in the
figure below is:
The value of the pronumerals c and d,
respectively, in the pair of congruent
triangles in the figure below is:
4
D
C
6.16
7.0
10.5
15.4
Maths Quest 10 for New South Wales 5.3 pathway
15 and 55o
7.5 and 25o
15 and 70o
15 and 110o
The test you could use to prove that
TRS  SUT is:
A
B
C
D
A
B
C
D
A
5
Chapter 5
SAS
AAS
RHS
SSS
ABC  RST
This means ACB =
A RST
B RTS
C SRT
D TRS
B
1
6
Which of the following triangles would
be congruent to ABC?
C
8
A trapezium is:
D
A. a parallelogram with one right
angle
B a quadrilateral with both pairs of
opposite sides parallel
C a rectangle with two adjacent sides
equal
D a quadrilateral with at least one pair
of opposite sides parallel.
9
Which of the following statements is
true?
A a square is a rectangle
B a rhombus is a square
C a parallelogram is a rectangle
D a trapezium is a square
A
10
Which of the following properties are
not true about a parallelogram?
A one pair of sides are parallel
B opposite angles are equal
C diagonals are equal
D opposite sides are equal
C
11
A quadrilateral is a rhombus if:
A all angles are equal
B diagonals bisect each other at right
angles
C diagonals are equal
D opposite angles are supplementary
B
12
If the diagonals of a quadrilateral bisect D
each other, then the quadrilateral is best
described as a:
A trapezium
B rectangle
C kite
D parallelogram
A
B
C
D
7
A parallelogram with two adjacent sides A
equal is:
A a rhombus
B a square
C a rectangle
D a trapezium
Maths Quest 10 for New South Wales 5.3 pathway
Chapter 5
2
Deductive geometry Test A
Name: ___________________________
Section B Short/Extended answer
1
Find the value of the pronumeral a in the pair
of similar triangles.
2
Find the value of the pronumerals b and c in the b  12 12

figure below.
13
6
12
b  12   13
6
b  12  26
b  26  12
b  14
c7 c

13
6
6c  42  13c
a 18

8 11
18
a  8
11
1
a  13
11
2
2
42  7c
c6
3
In the figure below show that ABC  ADC.
Maths Quest 10 for New South Wales 5.3 pathway
Chapter 5
AC is a common side
ACB = ACD (given as 90o)
BC = CD (given)
ABC  ADC (SAS)
3
3
4
Find the value of the pronumerals d and e in the Congruent triangles means all corresponding
following pair of congruent triangles.
sides and all corresponding angles are equal.
Therefore:
d=9
e = 10
3
5
Prove that if two angles of a triangle are equal,
then the sides opposite those angles are also
equal.
4
construct AD  BC
ABD = ACD (given)
ADB = ADC = 90 (given)
AD is common
 ABD  ACD (AAS)
 AB = AC (corresponding sides in congruent
triangles are equal).
 sides opposite the equal angles are also
equal.
Maths Quest 10 for New South Wales 5.3 pathway
Chapter 5
4
6
O is the centre of the circle.
Prove that SPO  MNO
SP = MN (given)
OP = OS = OM = ON (radii of the same circle
are equal)
3
SPO  MNO (SSS)
7
True or false?
(a) A parallelogram is a square.
(b) A square is a parallelogram.
2
(a)
(b)
false
true
8
Prove that PQRS is a parallelogram
PS = QR (given)
PS QR (since alternate angles are equal)
 PQRS is a parallelogram since one pair of
opposite sides are equal and parallel.
2
9
Prove that ABCD is a rhombus.
AM = MC and BM = MD (given)
 Diagonals bisect each other.
Since 32 + 42 = 52,
BMC = 90
 Diagonals bisect each other at right angles.
 ABCD is a rhombus.
3
10
Name any quadrilaterals whose diagonals
bisect the angles they pass through.
Rhombus and square
2
Maths Quest 10 for New South Wales 5.3 pathway
Chapter 5
5