Download Quadrilaterals and their properties

measurement anD Geometry • geometriC reasoning
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Quadrilaterals and their properties
FluenCY
1 We15 Name the following quadrilaterals, giving reasons for your answers.
a
b
c
Activity 5-E-1
Quadrilaterals
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Activity 5-E-2
More quadrilaterals
doc-1750
Activity 5-E-3
Advanced
quadrilaterals
doc-1751
d
e
f
This quadrilateral is a:
A square
B rectangle
C kite
D parallelogram
e rhombus
2 mC a
b
This quadrilateral is a:
A trapezium
B parallelogram
C rhombus
D kite
e square
c
This quadrilateral is a:
A trapezium
B square
C kite
D rhombus
e parallelogram
3 We16 Find the value of the pronumeral in each of the following diagrams.
a
b
t
42°
115°
110°
42°
138°
b
c
50°
d
18°
120°
t
t
162
maths Quest 7 for the australian Curriculum
20°
measurement anD Geometry • geometriC reasoning
e
f
54°
107°
107°
m
p
g
h
127°
32°
250°
12°
s
i
c
k
110°
93°
4 We17 Find the value of the pronumeral in each of the following diagrams, giving reasons for
your answers.
a
m
b
c
75°
132°
t
78°
u
d
e
108°
f
63°
73°
z
f
p
5 We18 Find the value of the pronumerals in each of the following diagrams.
a
b
98°
m
c
d
c
t
m
c
82°
t
64°
36°
Chapter 5
Geometry
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measurement anD Geometry • geometriC reasoning
d
e
106°
p
96°
f
75°
x
n
115°
p
m
91°
m
t
6 mC The value of t in the diagram at right is:
A 360è
B 112è
C 222è
D 138è
e 180è
t
42°
7 mC The value of r in the diagram at right is:
A 117è
B 180è
C 234è
D 126è
e 63è
117°
r
understanding
8 State whether each of the following statements is true or false.
a All squares are rectangles.
b All squares are rhombuses.
c All rectangles are squares.
d Any rhombus with at least one right angle is a square.
e A rectangle is a parallelogram with at least one angle equal to 90è.
9 mC A rectangle is a quadrilateral because:
A it has 4 right angles
C its opposite sides are equal in length
e it has 2 pairs of parallel sides and 4 right angles
B it has 2 pairs of parallel sides
D it has 4 straight sides
10 Draw 4 equilateral triangles with side lengths 4 cm and cut them out.
a Use 2 of these triangles to make a rhombus. Draw your solution.
b Use 3 of these triangles to make a trapezium. Draw your solution.
c Use all 4 triangles to make a parallelogram.
Draw your solution.
11 Copy and cut out the set of shapes shown at right.
Arrange the shapes to form a square. Draw your solution.
12 In your house, find an example of each type
of quadrilateral discussed in this section.
Write down the type of quadrilateral and
where you found it.
In the following questions, remember to provide coded
reasons for any relationships you form.
13 This photograph shows the roof of a fast food restaurant.
Calculate the value of p.
119°
p
164
maths Quest 7 for the australian Curriculum
measurement anD Geometry • geometriC reasoning
14 Find the size of the obtuse angle in the kite shown at right.
15 Two angles in a parallelogram are 45è and
135è. Find the other 2 angles.
16 Tom measures 2 angles of a kite at 60è
and 110è, but forgets which angle is which.
Draw 3 different kites that Tom may have
measured, showing the size of all angles in
each diagram.
65°
65
17 Below are sets of 4 angles. For each of the sets decide
whether it is possible to construct a quadrilateral.
Explain your answer.
a 25è, 95è, 140è, 100è
b 40è, 80è, 99è, 51è
18 Three angles of a quadrilateral are 60è, 70è and 100è.
a What is the size of the fourth angle of this quadrilateral?
b How many quadrilaterals with this set of angles are possible?
c Construct one quadrilateral with the given angle sizes in your book. (The choice of the
length of the sides is yours.)
reasoning
19 Val and Peter want to replace their front gate with another of the same design. To have this gate
made, they need to supply a diagram of it with all measurements and angles shown. Study the
photograph of Val and Peter’s gate and use it to help you answer the questions below.
8 cm
27°
18 cm
60 cm
1m
a There are 4 different shapes formed by the metal bars of the gate. How many different
types of triangles are there? Can you name them?
b How many types of quadrilaterals are there? Name them.
c Draw a diagram of the gate showing the length measurements and the one angle that is
given.
d Use this angle to calculate all the remaining angles in the diagram.
e Using a ruler and protractor, design a fence that is to be constructed using metal bars.
Include different triangles and quadrilaterals to
make your design as interesting as possible.
Write a short report describing the shapes
you have used and important angles which
need to be marked on your design to assist
in the construction of the fence.
reFleCtion
What would be an easy way to
remember the sum of angles in
quadrilaterals?
Chapter 5
Geometry
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