Symmetry & Shapes (Cambridge (CIE) IGCSE International Maths: Extended): Flashcards
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- FrontRotational Symmetry
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.
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.
Define a prism.
A prism is a solid with a uniform cross-section, meaning the cross-section is the same shape and size all the way through.
The cross-section does not have to be a polygon, so a cylinder is a prism with a circular cross-section.
Fill in the three missing words:
A
is a single surface of a 3D shape, an joins one corner to the next, and a is a corner itself.The completed sentence is:
A face is a single surface of a 3D shape, an edge joins one corner to the next, and a vertex is a corner itself.
The plural of vertex is vertices.
How many faces, edges and vertices does a cube have?
A cube has 6 faces, 12 edges and 8 vertices.
A cuboid has exactly the same numbers, because it is a cube that has been stretched along one or more directions.
True or False?
The three rectangular faces of a triangular prism are always identical.
False.
They are identical only when the triangular cross-section is equilateral.
If the triangle is isosceles only two of the rectangles are equal, and if it is scalene all three are different.
How many faces, edges and vertices does a triangular prism have?
A triangular prism has 5 faces, 9 edges and 6 vertices.
The 9 edges are the 3 sides of each triangle, plus the 3 edges joining the two triangles together.
Define a pyramid.
A pyramid is a solid with a flat base and sloping triangular sides that all meet at a single point, called the apex.
The base can be a square, a rectangle or a triangle.
True or False?
A tetrahedron has the same number of faces as it has vertices.
True.
A tetrahedron has 4 faces and 4 vertices, as well as 6 edges.
It is a triangular-based pyramid, so the base is a triangle too and every one of its four faces is a triangle.
What shape is the base of a cone, and what shape is the cross-section of a cylinder?
A cone has a circular base, and a cylinder has a circular cross-section all the way through.
A cone narrows to a point, so its cross-section gets smaller as you move up and is not uniform.
True or False?
A cylinder has no vertices.
True.
A cylinder has 0 vertices, because its two circular edges are curves that never meet at a corner.
It does still have 2 edges, one around each circular face.
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.
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