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.

Define a plane of symmetry .

A plane of symmetry is a flat surface that splits a 3D shape into two congruent halves which are mirror images of each other. A shape that has one is said to have reflection symmetry .

True or False? Every prism has at least one plane of symmetry.

True. Every prism can be cut in half halfway along its length , leaving two mirror-image pieces. That plane exists whatever the cross-section is, so no prism has none at all.

What changes when you look for rotational symmetry in 3D rather than 2D?

A 3D shape is rotated about an axis rather than about a centre point, and it may have a different order about different axes. A prism whose cross-section is an equilateral triangle has order 3 about the axis through the centre of that cross-section.

IGCSEMathsEdexcelMaths BFlashcardsGeometrySymmetry

Symmetry (Edexcel IGCSE Maths B): Flashcards

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What is rotational symmetry?

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Cards in this collection (14)

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:
1. Sketch the shape onto the tracing paper.
2. Draw an arrow pointing upwards on the tracing paper.
3. Place your pencil in the centre of the shape and rotate the tracing paper until the arrow is pointing upwards again (360º).
4. 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:
1. Trace the shape and the line of symmetry on the tracing paper.
2. Flip the paper over the line of symmetry.
3. The traced image will now be in its reflected position.
Define a plane of symmetry.
A plane of symmetry is a flat surface that splits a 3D shape into two congruent halves which are mirror images of each other.
A shape that has one is said to have reflection symmetry.
Fill in the number of planes of symmetry each solid has.
A cube has $______$ planes of symmetry, a cuboid has $______$ planes, and a cylinder has infinitely many.
The completed sentence is:
A cube has 9 planes of symmetry, a cuboid has 3 planes, and a cylinder has infinitely many.
The cuboid's three planes each cut it halfway between a pair of opposite faces, and the cube gains six more from its diagonal planes.
How many planes of symmetry does a prism have?
One more than the number of lines of symmetry in its cross-section.
Each line of symmetry gives a plane running along the prism, and one further plane cuts it halfway along its length.
So a prism with an equilateral triangle cross-section has $3 + 1 = 4$ , although the cube is a special case with 9 rather than 5.
How many planes of symmetry does a pyramid with a regular $n$ -sided base have?
It has $n$ of them, one for each line of symmetry in its base.
A square-based pyramid therefore has 4 planes of symmetry.
True or False?
Every prism has at least one plane of symmetry.
True.
Every prism can be cut in half halfway along its length, leaving two mirror-image pieces.
That plane exists whatever the cross-section is, so no prism has none at all.
What changes when you look for rotational symmetry in 3D rather than 2D?
A 3D shape is rotated about an axis rather than about a centre point, and it may have a different order about different axes.
A prism whose cross-section is an equilateral triangle has order 3 about the axis through the centre of that cross-section.

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