Mathematics 9: Transformations & Surface Areacreated by Ms. Hubbard (Riverside Secondary)

1.1 Line Symmetry

  • A line of is a mirror line that reflects an object onto itself, such that it is divided into two identical, reflective halves.

Example 1:Draw the lines of symmetry on the shapes below. What is the number of lines of symmetry for each shape?

a) b) c) d)

e) f)g) h)

Example 2:How many lines of symmetry do you find in:

  1. a square
/
  1. an isosceles triangle
/
  1. an equilateral triangle

Example 3:Complete a symmetric drawing (either by folding or reflecting) given one half of a shape. Draw in the line of symmetry.

a) b)

Example 4: Complete a symmetric drawing (either by folding or reflecting) given ¼ of the shape: Draw in all the resulting lines of symmetry and label the image points, ignore the labels of the points when considering symmetry.
a) b)

Example 5: Draw the mirror image of the statement so that it has a horizontal line of symmetry.

MATH IS AWESOME

1.2Rotation Symmetry

This figure has no lines of symmetry, yet we say it has rotation symmetry. What do you think that means?

  • A figure that can be mapped onto itself with a turn of less than one complete rotation has symmetry. The point about which the rotation of an object or design turns is called the center of rotation.
  • The number of times the figure matches with itself in a turn of 360 is the of the rotational symmetry. The order of rotation of a square is ______.
  • Rotational symmetry of order 2 is also called symmetry.
  • The angle of rotation is the smallest measure of an angle needed to turn a shape or design unto itself. If measured in degrees it is equal to 360 divided by the order of rotation. The angle of rotation of a square is

360 degrees ÷ 4 = 90 degrees OR 1 turn ÷ 4 = ¼ turn

Example 1:Write the order & angle of rotation symmetry for each figure below.

/ / / d.
e. / f. / g. / h.

Example 2: Symmetries in regular polygons. A regular heptagon has 7 equal sides and angles. What is the order of rotation, angle of rotation, and how many lines of symmetry does it have?

Example 3: Can a shape or design have both rotation and line symmetry?

# of lines of symmetry / Direction of lines of symmetry / order of rotation / angle of rotation
& fraction of a turn / type of symmetry
1.
2.
3.
4.
5.

Example 4: Complete the shading of each figure so that each design has the given order of symmetry.

Order 2 / Order 5 / Order 4 / Order 3

Do the shapes still have the given order if you shade the whole figure?

Example 5: Complete the picture so that it has rotation symmetry around the origin of order 2. Label the image points and state the angle of rotation.

a) b)

c) d)

Compare the coordinates of the original points to the coordinates of the image points? What do you notice? Do you think this happens for any angle of rotation around the origin?

Example 6: Complete the picture so that it has rotation symmetry around the origin of order 4. Label the image points and state the angle of rotation.

a) b)

c)d)

1.3Surface Area

Surface Area is the sum of the areas of all the faces (sides) of a 3-D Object.

1) In the following diagrams how many pieces have :

a) 4 faces showing? a) 3 faces showing?

b) 3 faces showing?b) 2 faces showing?

c) 2faces showing?c) 1 faces showing?

d) 1 faces showing?d) No faces showing?

1) Determine the surface area of the composite of cubes. Each cube has sides of 1 unit.

a) b)

c)d)

e) f)

g) h)

2) Determine the surface area of the composite of cubes. Each cube has sides of 2 units.

a) b)

3) Determine the surface area of the composite of cubes. Each cube has sides of 3 units.

a) b)

5) Determine the total surface area when the prisms are combined to form the composite object shown.

a) b)

6) Determine the surface are of the composite figures. (all measurements are in cm)

a)

b)

c)

d)

e)

f)

7) Determine the total area of overlap when the cylinders are combined to form the composite object shown.

a)b)

8) Determine the surface are of the composite figures. (all measurements are in cm)

a)

b)

c)

9) A bedroom with a rectangular shaped floor has a length of 8.5 feet, a width 9.5 feet and a height of 10 feet. It has one rectangular shaped door with dimensions 3 feet by 7 feet. Assuming there are no windows, find the surface area of the walls and ceilings. If one can of paint covers 175 feet squared, and you need to apply 2 coats of paint, how many cans of paint are required to paint the room?

10) A can of peas has a height of 10 and a circumference of . What amount of paper is needed to make labels for 20 cans of peas?

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