Define the term similar shapes.
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Define the term similar shapes.
Two shapes are similar if they have the same shape and their corresponding sides are in proportion.
One shape is an enlargement of the other.
True or False?
If two triangles of different sizes have the same angles they are not similar.
False.
If two triangles of different sizes have the same angles they are similar.
One is an enlargement of the other.
True or False?
Shapes that are not triangles can have the same angles and not be similar.
True.
Some shapes that are not triangles can have the same angles and not be similar.
E.g. two rectangles of different sizes will have the same angles but their corresponding sides could have different scale factors.
True or False?
To show that two non-triangular shapes are similar you need to show that their corresponding sides are in proportion.
True.
To show that two non-triangular shapes are similar you need to show that their corresponding sides are in proportion.
What is a scale factor, in the context of similarity?
A scale factor is the ratio of corresponding lengths in similar shapes.
True or False?
In the context of similarity, a scale factor cannot be negative.
True.
Although you can have a negative scale factor in general enlargement, in the context of similarity, a scale factor cannot be negative.
What does a scale factor that is greater than 0 but less than 1 imply?
A scale factor that is greater than 0 but less than 1 implies that the similar shape is smaller than the original shape.
How can you find a length scale factor?
A length scale factor can be found by dividing the length of a side on one shape by the length of a corresponding side on the similar shape.
What is rotational symmetry?
A shape is said to have rotational symmetry if, during a 360° rotation about its centre, it looks the same as it did in its original position.
What is meant by the order of rotational symmetry?
The order of rotational symmetry refers to the number of times a shape looks the same as it is rotated 360° about its centre.
True or False?
A shape can have order 0 rotational symmetry.
False.
A shape can never have order 0 rotational symmetry.
A shape is said to have no rotational symmetry when the order of rotational symmetry is 1, i.e. it only looks like its original position when it has been rotated through the full 360°.
How can tracing paper be used to help work out the order of rotational symmetry of a shape?
You can use tracing paper to help you work out the order of symmetry for a particular shape by doing the following:
Sketch the shape onto the tracing paper.
Draw an arrow pointing upwards on the tracing paper.
Place your pencil in the centre of the shape and rotate the tracing paper until the arrow is pointing upwards again (360º).
Count how many times the shape on the tracing paper maps over the shape on the paper beneath exactly; this is the order of rotational symmetry.
What is line symmetry?
A shape is said to have line symmetry when one half of the shape is a mirror image of the other half.
What is a line of symmetry?
A line of symmetry is a line across which a shape can be folded or reflected so that the two halves match exactly.
True or False?
A line of symmetry is also known as a line of reflection.
True.
A line of symmetry is also known as a line of reflection.
It can also be called a mirror line.
How can tracing paper be used to help sketch the reflection of a shape?
You can use tracing paper to help you sketch the reflection of a shape:
Trace the shape and the line of symmetry on the tracing paper.
Flip the paper over the line of symmetry.
The traced image will now be in its reflected position.
What is a geometrical proof?
A geometrical proof involves using known rules about geometry to prove a new statement about geometry.
How should each step in a geometrical proof be written?
Each step should be written in the form "[fact], [mathematical reason]".
It is really important to give a reason for each fact that you state.
E.g. Angle ABE = Angle CDE = 60º, vertically opposite angles.
There are a number of different rules or facts that you can use in geometrical proof.
Name three types of rules.
Any of the following types of rules may be used in geometrical proof:
Properties of 2D shapes (especially isosceles triangles and quadrilaterals)
Basic angle properties
Angles in polygons
Angles in parallel lines
Congruence and similarity
Circle theorems
Pythagoras' theorem