Transcript Quadrilaterals - mathsrevision

Level E
Quadrilaterals
This presentation will cover the basic properties
of various quadrilaterals. It is aimed at students
studying at level E (5-14).
Where appropriate, follow up exercises are indicated
for consolidation purposes.
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Quadrilaterals
Shape is
made up of 4
straight lines
Definition : Quadrilateral is “ A closed 4 sided linear shape”
A few types of special quadrilaterals
Square
Rhombus
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Rectangle
Parallelogram
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Quadrilateral
Kite
Trapezium
2
Starter Questions
Q1.
Solve the equation below
x  21  32
a
o
Q2.
Find all the missing angles
Q3.
Find the average of the numbers below
b
o
2,5,6,7,5,2,2,5,6,7,5,8
Q4.
Find
30% of £240
Friday, 17 July 2015
Created by Mr.Lafferty
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Quadrilaterals
Shape is
made up of 4
straight lines
Definition : Quadrilateral is “ A closed 4 sided linear shape”
A few types of special quadrilaterals
Square
Rhombus
Friday, 17 July 2015
Rectangle
Parallelogram
Created by Mr.Lafferty
Kite
Trapezium
4
The Square
Properties of a square
l
(a)
(b)
(c)
(d)
l
l
(e)
l
(f)
Area  l  l  l
2
Perimeter  l  l  l  l  4l
(g)
(h)
(i)
(j)
4 sides are equal length
Opposite sides are parallel
o
All angles are equal and are 90
It has 4 line of symmetry
1
2
1
4
Turn symmetry
Turn symmetry
If cut out it can fit back 8
different ways
Two diagonals are the same length
o
Diagonals bisect each other at 90
Diagonals bisect corner angles
Exercise 1 Teejay Page 209
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Created by Mr.Lafferty
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Starter Questions
Q1.
Calculate
540  9
o
105
Q2.
Find all the missing angles
Q3.
List the prime numbers between 50 and 60
Q4.
Find
15% of £400
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Created by Mr.Lafferty
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The Rectangle
Properties of a rectangle
l
b
b
l
Area  length  breadth  l  b
Perimeter  l  b  l  b  2l  2b
(a)
Opposite sides have equal length
(b)
Opposite sides are parallel
(c)
All angles are equal and are 90
(d)
It has 2 line of symmetry
(e)
1
2
(f)
(g)
If cut out it can fit back 4
different ways
Diagonals are the same length
(h)
Diagonals bisect each other
o
Turn symmetry
Exercise 2 Teejay Page 210
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Starter Questions
Q1.
List 4 properties of a square.
Q2.
Simplify the following fraction
Q3.
Express the following percentages as fractions
(a ) 25%
Q4.
35
100
(b) 12.5%
Solve
2x  4  22
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Angles in a Quadrilateral
IMPORTANT : The angles in a quadrilateral ALWAYS add up to 360
o
a o  b o  c o  d o  360o
B
b
o
o
c
ABC
o
A
ACD
and
a
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o
d
D
C
We have split the quadrilateral into two triangles
But for any triangle
0
the sum of the angles is 180
o
o
Hence for the quadrilateral we have 2x180 =360
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Angles in a Quadrilateral
Question : Find the missing angle below.
The four angles of a quadrilateral add to = 360
w
z
34
100
o
o
y
y
o
x
90o  34o  100o  y o  360o
y o  360o  224o
y o  136o
Exercise 3 Teejay Page 213
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o
Starter Questions
Q1.
List 4 properties of a rectangle.
Q2.
Find the mean and range of the numbers 3,4,5
Q3.
Express the following decimals
(a ) 25%
Q4.
(b) 12.5%
Tidy up the following
2x 2  4x  6x 2  5x  y  3y 2
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The Rhombus
Properties of a rhombus
l
l
l
l
(a)
All sides have equal length
(b)
Opposite sides are parallel
(c)
Opposite angles are equal
(d)
It has 2 line of symmetry
(e)
1
2
(f)
If cut out it can fit back 4
different ways
o
Diagonals bisect each other at 90
Diagonals bisect corner angles
(g)
(h)
Turn symmetry
Exercise 4 Teejay Page 214
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Starter Questions
18
 6 4
2
Q1.
Calculate
Q2.
If 1 bar of chocolate costs 65p. How much will
1000 bars cost. Give your answer in £’s.
Q3.
A football player scores an average of 1.5 goals
a game. How many goals should he score over
10 games.
Q1.
Find
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2
60% of £300
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The Kite
B
l1
Properties of a kite
l1
A
C
l2
l2
D
(a)
2 pairs of adjacent sides of equal length
(b)
Left and right angles are the same
(c)
It has 1 line of symmetry
(d)
If cut out it can fit back 2
different ways
(e)
Only one diagonal bisects the other
(f)
Diagonals cross each other at 90
(g)
One diagonal bisect corner angles
o
Exercise 1 Teejay Page 218
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Created by Mr.Lafferty
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Starter Questions
Q1.
List 4 properties of a Rhombus
Q2.
How many seconds in 2 days
Q3.
Find the range and the mean of the numbers below
4,2,4,6,8,15,3
Q4.
Calculate
a b c
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a = -2 , b = -3 c = 6
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The Parallelogram
Properties of a parallelogram
l1
B
C
l2
A
l2
D
l1
(a)
Opposite pairs of sides have equal length
(b)
Opposite pairs of sides are parallel
(c)
Opposite pairs of angles are equal
(d)
1
2
(e)
It has NO lines of symmetry
(f)
If cut out it can fit back 2 different ways
(g)
Diagonals bisect each other
Turn symmetry
Exercise 1 Teejay Page 221
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Starter Questions
Q1.
Which letter has half-turn symmetry
A,C,H,P
Q2.
7
7
Find all the missing angles
7
Q1.
Name 2 equilaterals that have all angles equal.
Q1.
Find
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3
of £200
5
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The Trapezium
Properties of a trapezium
Has ONLY ONE property which is
1 pair of parallel lines
Exercise 1 Teejay Page 224
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Ink Exercise
Topic in a Nutshell
Page 225
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