1. Angles

2. Starter Identify 5 right angles in the classroom?
How many right angles are there around a point?
How many degrees are in a right angle?
How many degrees are there around a point?
How many right angles are
there on this flag? 16
360 90 4
Door corner, book corners, desk corner……

3. Classroom Expectations
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

4. Vocabulary
Vertex
Arm

5. C A T
We name this angle
Ex Question 2,3

6. An angle measures the amount a line has to turn to fit onto another line
We measure angles
in degrees.

7. Vocabulary to do with Angle Sizes
An acute angle is between 0 and 90 degrees

8. A right angle is 90 degrees

9. An obtuse angle is between 90 and 180 degrees

10. A straight angle is 180 degrees

11. A reflex angle is between 180 and 360 degrees
Do Exercise go onto if finished

12. 105°
180°
90°
24°
150°
348°
78°
248°
Obtuse
Acute
Reflex
Right Angle
Straight

13. Obtuse
Acute
Reflex
Right Angle
Straight
150°
105°
78°
24°
248°
348°
90°
180°

14. We generally measure angle in degrees with a protractor
Exercise do any 5

15. Angle Winner Example(1) 45 50 42 Amy 1 2 3 4 5 6 7 8 Jade Estimation
Kate Estimation
Exact size
Winner
Example(1) 45 50 42
Amy 1 2 3 4 5 6 7 8

16. Complementary Angles are angles that add to 90°.
55°
X=35°
x=?

17. Adjacent angles on a straight line sum 1800
1200
600
Supplementary angles

18. 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

19. Angles in a Triangle
Angles in a triangle sum 1800

20. Two different objects with acute angles
Four different objects with right angles
Two different objects with obtuse angles
One straight angle
Two different reflex angles around the room
Bonus Question
Can you find any angles that are
complementary or supplementary?

21. Angles around a point sum 3600
1200 a
1600
a = 80 degrees

22. Vertex Vertically opposite angles Are opposite each other at a vertex
They are equal

23. Page 378 and 380
Exercise and 25.10

24. Angles on parallel lines
Transversal

25. Corresponding angles are congruent
1000 a
a = 100 degrees

26. Co-interior angles sum 1800
720
g = 108 degrees

27. k
700
Alternate angles are congruent
K = 70 degrees

28. Starter!!!
You can choose to do the left hand side or the right hand side.
50º
70º B= A= C=
120º C= A= B=
A=____
B=____
C=____
D=____
E=____
60º
50º
70º
85º
60º E=
30º E=
90º D= D=
A=____
B=____
C=____
D=____
E=____
70º
110º
70º
95º
95º

29. Beta Book
Page 246 Ex

30. Game Rules 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

31. 3D Shapes

32. Starter
Name the following shapes and give examples of them from your life.

33. Face Edges and Vertices Hidden Lines

34. Exercises
Page 457
Exercise 29.01
Questions 4, 6, 9,14 and 15

35. Answers from Text Book 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

36. 6 12 8 5 9 18 7 15 10 Shape No. Faces Edges Vertices a Cube b
Triangular Prism 5 9 C
Hexagonal Prism 18 d
Pyramid e
Cube where a triangular slice has been cut off. 7 15 10
Barton, D., Alpha Mathematics Second Edition

37. Isometric Drawings

39. Starter

40. Tetracubes 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

42. Views
Top
Right
Left
Left
Front
Right 1 1 1 1
Front
Plain View

43. 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.

44. Front
Right
Try and make this shape!!! (Then draw it)
Left
Top

45. Front
Left
Right
Top
Views
Right
Left
Front
Plain
View 2 1 3

46. Notes if you want them!!!
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.

48. Views
Left
Top
Plain
View 2 1 3
Front
Right

49. Nets
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.

51. Instructions 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?

52. Make Your Cubes!!!!!

53. Further 3D Shapes

54. Closed figures made up of straight sides.
Polygons
Closed figures made up of straight sides.

55. Examples of Polygons Triangle Quadrilateral Pentagon Hexagon Octagon
Decagon

56. Angles of Polygons 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.

57. Exterior Angles Measure the exterior angles of your polygons.d
Exterior Angles
Measure the exterior angles of your polygons.
Add the exterior angles of each shape together.
What do they add to?
Shape
Total Degrees of Exterior Angles
Triangle
Quadrilateral
Pentagon
Hexagon
360
The sum of the exterior angles of a polygon is 360°.

58. Adjacent angles on a straight line
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

59. 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.

60. Interior Angles of a Polygon
ttrsgf
Interior Angles of a Polygon
No. of sides of polygon 3 4 5
You do 6, 8, 10
Drawing
Number of triangles 1 2
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

61. Regular Polygons
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.

62. Exterior Angles Number of sides Sum of exterior angles
Each exterior angle
Equilateral triangle
Square
Pentagon
Hexagon
Octagon
Decagon 3 4 5 6 8 10
360
120 90 72 60 45 36
Interior Angles
Number of sides
Sum of exterior angles
Each exterior angle
Equilateral triangle
Square
Pentagon
Hexagon
Octagon
Decagon
180
360
540
720
1080
1440 60 90
108
120
135
144 3 4 5 6 8 10

63. Navigation and Bearings

64. Bearings
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

65. Bearings

69. Starter

76. Paper Cutting

78. Translation
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.

79. A B E’ F’ B’ D’ C’ G’ A' G F E D C

80. Reflection
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

81. m

82. Where would the mirror line go??

83. Invariant Points
If a point is already on the mirror line, it stays where it is when reflected. These points are called invariant points.

84. m m

85. Exercises Today 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 Page 404

86. Rotation
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.

87. 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.

88. D A C B D’ A’ B’ C’

89. Rotation

90. What are these equivalent angles of Rotation?
Rotations are always specified in the anti clockwise direction
What are these equivalent angles of Rotation?
270º Anti clockwise is _______ clockwise
180º Anti clockwise is ______ clockwise
340º Anti clockwise is _______ clockwise

91. Rotation
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.

92. Drawing Rotations
¼ turn clockwise = B C
90º clockwise A B’ D D’ C’

93. Drawing Rotations ¼ Turn anti-clockwise = 90º Anti-clockwise C’ B C A

94. Define these terms The line equidistant from an object and its image
The point an object is rotated about
Doesn’t change
Mirror line
Centre of rotation
Invariant
What is invariant in
Reflection
rotation
The mirror line
Centre of rotation

95. 180º By what angle is this flag rotated about point C ?
Remember: Rotation is always measured in the anti clockwise direction!

96. By what angle is this flag rotated about point C ?
90º

97. By what angle is this flag rotated about point C ?
270º

98. Questions Ex 26.07 Page 411 Qn 1, 2, 3, 7 and 8.

99. Answers 26.07 1 D C B’ C’ D’ B A’ A A’ C’ C 2 B’ A B

100. C D 3 A B’ A’ B D C D’ C’ B A C’ B’ 7 D’ A’

101. s s 8

102. Ex
a) P b) R c) QS
180°
0° or 360°
8. a) R b) Q c) CB

103. Rotational Symmetry
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.

104. Order of rotational symmetry=4 3

105. Line Symmetry
A shape has line symmetry if it reflects or folds onto itself.
The fold is called an axis of symmetry. 2
Line symmetry=

106. Total order of symmetry
The number of axes of symmetry plus the order of rotational symmetry.
2+2=4

108. -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 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 1 2 3 4 5 6 7 8
1. Move the green dot by the following values and state where it now lies.
(-6), (3), (-9), (-4) and (5).

109. Groups 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

110. Translations Each point moves the same distance in the same direction
There are no invariant points in a translation
(every point moves)

111. ( ) Vectors describe movement + + - - x y
← movement in the x direction (right and left) y
← movement in the y direction (up and down)

112. ( ) Vectors Vectors describe movement
Each vertex of shape EFGH moves along the vector
( ) -3 -6
To become the translated shape E’F’G’H’

113. Translate the shape ABCDEF by the vector to give the image A`B`C`D`E`F`.
( )
- 4
- 2

114. Vectors +3 +4 -5 +4 +2 -6 -6 -2