Define the term congruent.
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Define the term congruent.
Two shapes are congruent if they are identical in shape and size.
True or False?
If one shape is an enlargement of the other, then they are congruent.
False.
If one shape is an enlargement of the other, then they are not identical in size and so are not congruent.
True or False?
You need to show that two shapes are facing in the same direction to prove congruence.
False.
If the two shapes are identical in terms of shape and size then it does not matter which direction they are facing in.
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.
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.
Define the term scale factor.
A scale factor is the ratio of corresponding lengths in similar shapes.
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.
Define 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 the centre of rotation?
The centre of rotation is the fixed point about which a shape is rotated.
What is 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
Define 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 by tracing over the shape, then flipping it over the line of reflection to see how the shape will reflect.
What is a geometrical proof?
A geometrical proof is a step-by-step process of logical reasoning using known rules in order prove a new statement about geometry.
True or False?
A proof question might start with "Prove..." or "Show that ...".
True.
A proof question will commonly start with "Prove..." or "Show that ...".
What is the format for writing each proof step?
Write each step in the form "[fact] , [mathematical reason]".
For example, "AB = CD, opposite sides of a rectangle are equal length".
How should you refer to an angle in a diagram?
An angle that is formed by the lines AB and BC can be referred to by writing "angle ABC" or "∠ABC".
What mathematical rules might you need to use to complete a proof?
Common rules that you might need to use include:
Properties of 2D shapes
Basic angle properties
Angles in polygons
Angles in parallel lines
Congruence and similarity
Circle theorems
Pythagoras' theorem.