Download Angles


Identify 5 right angles in the classroom?
Door corner, book corners, desk corner……




4
How many right angles are there around a
point?
90
How many degrees are in a right angle?
360
How many degrees are there around a point?
How many right angles
are
16
there on this flag?








Show respect to all other people and property
Be on time to class
Bring all necessary equipment to class
Enter the room sensibly
Listen in silence when the teacher or another
student is talking
Raise your hand when you want to ask or
answer a question
Work without disturbing others
Complete all homework
Vocabulary
Vertex
Arm
C
We name this angle
CÂT
A
T
Ex 25.02 Question 2,3
An angle measures
the amount a line
has to turn to fit
onto another line
We measure angles
in degrees.
Vocabulary to do with
Angle Sizes
An acute angle is
between 0 and 90
degrees
A right angle is 90
degrees
An obtuse angle is
between 90 and
180 degrees
A straight angle is 180
degrees
A reflex angle is
between 180 and
360 degrees
Do Exercise 25.05 go onto
25.06 if finished
150°
Obtuse
Acute
Reflex
Right Angle
Straight
248°
105°
78°
90°
24°
348°
180°
Obtuse 150° 105°
Acute
78° 24°
Reflex 248° 348°
Right Angle90°
Straight 180°
We generally measure angle in
degrees with a protractor
110
degrees
Exercise 25.04 do any 5
Angle
Jade
Estimation
Kate
Estimation
Exact
size
Winner
Example(1
)
45
50
42
Amy
1
2
3
4
5
6
7
8
Complementary Angles are angles that
add to 90°.
55°
x=?
X=35°
Adjacent angles on a straight line
sum 1800
1200
600
Supplementary angles
Activity
Draw a straight line on your paper.
Name each angle of your triangle. One A,B and C
Tear, (or cut) the angles (corners) away from your paper and lay them
out alone the line.
C
A
B
Angles in a Triangle
Angles in a triangle sum 1800
1.Two different objects with acute angles
2.Four different objects with right angles
3.Two different objects with obtuse angles
4.One straight angle
5.Two different reflex angles around the room
Bonus Question
Can you find any angles that are
complementary or supplementary?
Angles around a point sum 3600
1200
a
a = 80 degrees
1600
Vertically opposite angles
Are opposite each other at a vertex
They are equal
Vertex
Page 378 and 380
Exercise 25.09 and 25.10
Angles on parallel lines
Transversal
Corresponding angles are congruent
1000
a
a = 100 degrees
Co-interior angles sum 1800
g
720
g = 108 degrees
k
700
Alternate angles are congruent
K = 70 degrees
Starter!!!
50º
You can choose to do the left hand side or the right hand side.
70º
B=
C=
C=
60º
A=____
50º
B=____
C=____
70º
30º
D=____
E=____
90º
120º
A=
E=
A=
B=
85º
E=
60º
D=
D=
70º
A=____
110º
B=____
70º
C=____
95º
D=____
95º
E=____


Page 246
Ex. 18.07




Have a counter on each of the spots.
The first player can remove 1 or 2 counters
off the board (if they take two they must be
connecting dots.)
The winner is the player who picks up the last
counter!!!
Play a few games and try to work out a
winning strategy

Name the following shapes and give
examples of them from your life.



Page 457
Exercise 29.01
Questions 4, 6, 9,14 and 15

4- a) 4 b) 6 c) 4
6- Draw on the board
9- Next Page
14- Tetrahedron
15- a) Trapeziums b) 12 c) Pyramid

Barton, D., Alpha Mathematics Second Edition




Shape
No.
Faces
No.
Edges
No.
Vertices
a
Cube
6
12
8
b
Triangular Prism
5
9
6
C
Hexagonal Prism
8
18
12
d
Pyramid
5
8
5
e
Cube where a
triangular slice has
been cut off.
7
15
10
•Barton, D., Alpha Mathematics Second Edition




A solid made up of four identical cubes
joined face to face
There are eight different tetracubes
Make each tetracube then draw it in your
isometric paper
Make sure you don’t just draw the same
tetracube from a different angle
Top
Right
Left
Left
Front
Right
1
1 1
1
Plain View
Front
Right
Front
Left
Draw your own copy of this block formation on your isometric paper
Draw the front, left, right and top views
Draw the plan view of the shape.
Front
Right
Try and make this shape!!! (Then draw it)
Left
Top
Front
Right
Right
Left
Front
Left
Plain
View
2
2
3
1
2
Top


Plain View- shows the height of different
parts of the solid when viewed from above.
There are also profile views which show the
shape from one side only.
Plain
View
2
2
Left
Front
3
2
1
Top
Right



A plan that shows all the faces of a solid. It
shows how all the faces could be folded and
joined to make the shape.
Dashed lines show where to fold.
Often tabs are included for ease of
constructing the shape from the net.




Make a net for a closed cube.
How many faces does a closed cube have?
What is the smallest number
of tabs that you could use
so that every joint is secure?
What coloured square will
be on the opposite side of the cube
from the green one?
Closed figures made up of straight sides.






Triangle
Quadrilateral
Pentagon
Hexagon
Octagon
Decagon

Interior angles- are
angles
between the sides of
the
polygon on the
inside.
• Exterior angles- are angles
found by extending the
sides of the polygon.
•
•
•
Measure the exterior angles of your polygons.
Add the exterior angles of each shape
together.
What do they add to?d
Shape
Total Degrees of
Exterior Angles
Triangle
360
Quadrilateral
360
Pentagon
360
Hexagon
360
The sum of the exterior angles of a polygon is 360°.
Alternate angles
When two parallel lines
are cut by a third line,
then angles in alternate
positions equal in size.
Co-interior
angles
When two parallel lines
are cut by a third line,
co-interior angles are
supplementary.
Angles at a point.
The sum of the sizes of the
angles at a point is 360
Adjacent angles
on a straight line
The sum of the sizes of the
angles on a line is 180
degrease
Adjacent angles
in a right angle
The sum of the size's of the
angles in around different
points but the same angle
Vertically
opposite angles
Vertically opposite angles
are equal in size.
Corresponding
angles
When two parallel lines are
cut by a third line, then
angles in corresponding
positions are equal in size.
No. of
sides of
polygon
3
4
5
You do 6,
8, 10
Drawing
ttrsgf
Number of
1
2
3
triangles
Degrees in a triangle sum to 180°
If there are 180 degrees in a triangle how many degrees must there
Be in a quadrilateral which is split into 2 triangles.
The rule (n2) × 180°
n is the number of sides
of the polygon
A polygon is called regular if all its sides are
the same length and all its angles are the
same size.
e.g. equilateral triangle, a square or a regular
pentagon.

Exterior Angles
Number of
sides
3
4
5
6
8
Equilateral triangle
Square
Pentagon
Hexagon
Octagon
Decagon
Interior Angles
Equilateral
triangle
Square
Pentagon
Hexagon
Octagon
Decagon
10
Number of
sides
3
4
5
6
8
10
Sum of exterior Each exterior
angles
angle
36
120
0
90
36
72
0
60
36
45
0
36
36
0
36
Sum0of exterior Each exterior
angles
36
180
0
360
540
720
108
0
144
0
angle
60
90
108
120
135
144


Bearings are angles which are measured
clockwise from north. They are always written
using 3 digits.
The bearings start at 000 facing north and
finish at 360 facing north.
Bearings
045
120
180
270


A translation is a movement in which each
point moves in the same direction by the
same distance.
To translate an object all you need to know is
the image of one point. Every other point
moves in the same distance in the same
direction.
A
B
G
A'
B’
G’
F
F’
E
E’
D
C
D’
C’


In a reflection, and object and its image are
on opposite sides of a line of symmetry.
This line is often called a mirror line.
m
m
m

If a point is already on the mirror line, it stays
where it is when reflected. These points are
called invariant points.
m
m



Ex 26.03 2 of 1a, b, c or d. Page397
26.04 Question 2, 7 and 8. Page 401 & 402
Any three questions from 26.05. Page 404



Rotation is a transformation where an object
is turned around a point to give its image.
Each part of the object is turned through the
same angle.
To rotate an object you need to know where
the center of rotation is and the angle of
rotation.


This can be given in degrees or as a fraction
such as a quarter turn.
The direction the object is turned can be
either clockwise or anti-clockwise.
A
B
C
D
C’
D’
A’
B’
Rotations are always specified in
the anti clockwise direction



270º Anti clockwise is _______ clockwise
180º Anti clockwise is ______ clockwise
340º Anti clockwise is _______ clockwise




In rotation every point rotates through a
certain angle about a fixed point called the
centre of rotation.
Rotation is always done in an anti-clockwise
direction.
A point and it’s image are always the same
distance from the centre of rotation.
The centre of rotation is the only invariant
point.
B
¼ turn clockwise =
C
90º clockwise
A
D’
D
B’
C’
¼ Turn anti-clockwise = 90º Anti-clockwise
C’
B
C
B’
A
The line equidistant from an
Mirror line
object and its image
 Centre of rotation
The point an object is rotated
 Invariant
about
Doesn’t change
What is invariant in
 Reflection


rotation
The mirror line
Centre of rotation
By what angle is this flag rotated about point C ?
C
180º
Remember: Rotation is always measured in the anti clockwise direc
By what angle is this flag rotated about point C ?
C
90º
By what angle is this flag rotated about point C ?
C
270º


Ex 26.07 Page 411 Qn 1, 2, 3, 7 and 8.
Ex 26.08 Page 412 Qn 1, 3, 4 and 6.
1
D
C’
B’
D’
A’ A
C
B
A’
C’ C
2
B’
A
B
C
D
3
B’
C’
A
A’
D
B
C
D’
7
A
C’
D’
B
B’
A’
s
s
8
1.
a) P b) R c) QS
3.
180°
4.
0° or 360°
8. a) R b) Q c) CB


A figure has rotational symmetry about a
point if there is a rotation other than 360°
when the figure can turn onto itself.
Order of rotational symmetry is the number
of times a figure can map onto itself.
Order of rotational symmetry=
4
Order of rotational symmetry=
3


A shape has line symmetry if it reflects or
folds onto itself.
The fold is called an axis of symmetry.
Line symmetry=
2

The number of axes of symmetry plus the
order of rotational symmetry.
2+2=4
8
7
6
5
-4 -3
2
1
0
1
2
3
4
5
6
7
8
7
8
1. Move the red dot by the following values and state where it
now lies.
(-1), (4), (7), (-4) and (11).
8
7
6
5
-4 -3
2
1
0
1
2
3
4
5
6
1. Move the green dot by the following values and state where it
now lies.
(-6), (3), (-9), (-4) and (5).






Group One- Kelly, Ruby, Bella, Chrisanna
and Bianca
Group Two- Hannah B, Grace, Shanice,
Grace and Georgia R
Group Three- Hannah C, Remy, Olivia,
Kendyl and Sarah
Group Four- Kelsey, Shaquille, Kiriana,
Cadyne and Claudia
Group Five- Lauran, Ashlee, Sophie, Georgia
W and Emily S
Group Six- Esther, Emily M, Jemma, Amelia
and Julia
Each point
moves the same
distance in the
same direction
There are no
invariant points
in a translation
(every point
moves)
• Vectors describe movement
+
+
-
()
x
y
-
← movement in the x direction (right and left)
← movement in the y direction (up and down)

Vectors describe movement
Each vertex of shape EFGH
moves along the vector
()
-3
-6
To become the translated shape E’F’G’H’

Translate the shape ABCDEF by the vector to
give the image A`B`C`D`E`F`.
()
-4
-2
-5
+4
+2
-6
+3
+4
-6
-2