Symmetry & Shapes (AQA GCSE Maths)
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What is rotational symmetry?
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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 plane of symmetry in a 3D shape?
A plane of symmetry in a 3D shape is a plane (flat 2D shape) that splits a 3D shape into two congruent (identical) halves that are mirror images of each other.
How many planes of symmetry does a cube have?
A cube has 9 planes of symmetry.
How many planes of symmetry does a cuboid have?
A cuboid has 3 planes of symmetry.
How many planes of symmetry does a square-based pyramid have?
A square-based pyramid has 4 planes of symmetry.
True or False?
A cylinder has infinite rotational symmetry.
True.
A cylinder has infinite rotational symmetry about the axis that runs through the centre point of both circular faces.
True or False?
The circumference of a circle is the perimeter of the circle.
True.
The circumference of a circle is the perimeter of the circle.
It is the length around the outside of the shape.
What is the name for the line of symmetry of a circle?
A circle's line of symmetry is known as the diameter.
A diameter of a circle is a line that touches the circumference at either end and passes through the centre of the circle.
How many sides does a decagon have?
A decagon has 10 sides.
What are the defining properties of a parallelogram?
A parallelogram is a quadrilateral with:
two pairs of equal, opposite angles,
and two pairs of opposite, parallel sides.
(Each pair of opposite parallel sides are also of equal length.)
What are the defining properties of a rhombus?
A rhombus is a quadrilateral with:
two pairs of equal, opposite angles,
two pairs of opposite, parallel sides,
and four sides of equal length.
True or False?
The diagonals of a rectangle bisect each other at the centre of the rectangle.
True.
The diagonals of a rectangle bisect each other at the centre of the rectangle.
What are the defining properties of a trapezium?
A trapezium is a quadrilateral with:
one pair of opposite, parallel sides of unequal length.
What are the defining properties of a kite?
A kite is a quadrilateral with:
one line of symmetry,
one pair of equal angles opposite the main diagonal,
and two pairs of equal, adjacent sides.
True or False?
The diagonals of a rhombus bisect each other at right angles (90°).
True.
The diagonals of a rhombus bisect each other at right angles (90°).
True or false?
If a trapezium has a line of symmetry it is an isosceles trapezium.
True.
If a trapezium has a line of symmetry it is an isosceles trapezium.
What is a vertex on a 3D shape?
A vertex is a corner of a 3D shape.
E.g. a square-based pyramid has 5 vertices.
What is a face on a 3D shape?
A face is an individual flat surface of a 3D shape.
E.g. a cylinder has 2 circular faces (the two 'ends'), along with one curved surface.
What is a prism?
A prism is a 3D shape with the same cross-section throughout.
E.g. a cuboid is a rectangular prism.
True or False?
A cuboid has six equal, square faces.
False.
A cuboid has six rectangular faces.
They consist of three pairs of equal rectangular faces.A cube has six equal, square faces.
What does a net of a 3D shape represent?
A net of a 3D shape is a 2D pattern that could be folded to make that 3D shape.
How many edges are there on a square-based pyramid?
There are eight edges on a square-based pyramid.
True or False?
The base of a tetrahedron is a square.
False.
The base of a tetrahedron is a triangle.
What shape is the cross-section of a cylinder?
The cross-section of a cylinder is a circle.
True or False?
A triangular prism has two equal triangular faces and three rectangular faces.
True.
A triangular prism has two equal triangular faces and three rectangular faces.
True or False?
A cube is a type of prism.
True.
A cube is a type of prism with a square cross-section.
What are plans and elevations?
Plans and elevations are two-dimensional views of a three-dimensional object.
Define the term plan view.
Plan view is the view you would see looking directly down on an object. It is also commonly known as a bird's-eye-view.
What is a front elevation?
A front elevation is the shape you would see if you stood directly in front of the object.
Define the term side elevation.
Side elevation is the shape you would see if you were directly facing the side of the object.
True or False?
The front elevation shows the object as seen from directly above.
False.
The front elevation does not show the object as seen from directly above.
The front elevation shows the object as seen from directly in front. It is the shape you would see if you stood directly in front of the object.
What is the purpose of using different colours or shading in isometric drawings?
Using different colours or shading in isometric drawings helps to distinguish between the three views and identify hidden parts more easily.
True or False?
The plan view always shows the largest face of an object.
False.
The plan view does not always shows the largest face of an object.
The plan view shows the top view of an object, which may not always be the largest face.