On a diagram, what do arrows drawn on two lines mean, and what do tick marks mean?

Arrows show that the lines are parallel ; tick marks show that the lines are equal in length . Where a diagram has a second, separate pair of each, double arrows and double ticks are used to keep the two pairs apart.

What does it mean for two lines to be perpendicular ?

They intersect at right angles , meaning the angle between them is 90°. On a diagram this is marked with a small square at the point where they cross.

True or False? An angle of 200° is called a reflex angle.

True. Any angle greater than 180° but less than 360° is reflex . An angle of exactly 180° is a straight angle, so reflex angles pick up where that leaves off.

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.

A square is a special kind of rectangle, and a rhombus is a special kind of parallelogram. What do both special cases have in common?

In each case, all four sides are the same length . A rectangle and a parallelogram each have two pairs of equal sides; making all four equal is what produces the square and the rhombus.

A quadrilateral has exactly one pair of parallel sides. What is it called, and what is it called if it has two pairs?

One pair of parallel sides makes it a trapezium . Two pairs of parallel sides make it a parallelogram .

How are the equal sides of a kite arranged, compared with those of a parallelogram?

A kite's equal sides are adjacent , meaning next to each other, in two pairs. A parallelogram's equal sides are opposite each other, and unlike a parallelogram a kite has no parallel sides at all.

What does it mean to say that a diagonal bisects another?

It cuts the other diagonal exactly in half, crossing it at its midpoint. In a square, rectangle, parallelogram and rhombus each diagonal bisects the other; in a trapezium neither does.

In which quadrilaterals are the two diagonals perpendicular ?

In the square , the rhombus and the kite . In a rectangle, a parallelogram and a trapezium the diagonals cross at some other angle.

True or False? The two diagonals of a kite bisect each other.

False. Only one of a kite's diagonals bisects the other. The longer diagonal cuts the shorter one in half, but the shorter one does not return the favour.

Define a chord of a circle.

A chord is a straight line joining two points on the circumference. It does not have to pass through the centre, and it does not extend beyond the circle.

Define a segment of a circle.

A segment is the region enclosed between a chord and the arc that the chord cuts off. Every chord creates two segments, a larger one and a smaller one.

Define a tangent to a circle.

A tangent is a straight line that touches the circumference at exactly one point . Unlike a chord, it does not cut across the circle at all.

True or False? Every diameter is also a chord.

True. A diameter joins two points on the circumference, which is exactly what a chord does. A diameter is simply the special chord that passes through the centre , and it is the longest chord a circle has.

Why is a diameter a line of symmetry of a circle?

Because it passes through the centre , so it splits the circle into two identical halves. A circle has infinitely many lines of symmetry, since every diameter is one.

A prism is a 3D shape with the same cross-section all the way through its length. The cross-section of a cube is a square, and that of a cuboid is a rectangle.

Why is a cylinder described as being similar to a prism?

Because it also has the same cross-section all the way through, in its case a circle. Its two circular ends are identical, exactly as a prism's two ends are.

True or False? The three rectangular faces of a triangular prism are always equal to one another.

False. All three are equal only when the triangular ends are equilateral . If the triangular ends are isosceles then only two of the rectangles match, because the rectangles take their widths from the sides of the triangle.

Define the net of a solid.

A net is a 2D drawing that can be cut out and folded up to make the 3D shape. Each face of the solid appears once in the net, arranged so that the right edges meet when it is folded.

How is the area of a net related to the solid it folds into?

The area of the net is exactly the surface area of the solid. Folding does not change how much material there is, it only rearranges it in space.

True or False? Any arrangement of six squares joined edge to edge will fold up into a cube.

False. Only 11 different arrangements of six squares actually fold into a cube. A solid can have more than one net, but not every arrangement of the right faces is one.

What shapes make up the net of a cylinder , and what are the rectangle's dimensions equal to?

Two circles and one rectangle . The rectangle's length is the circumference of the circles, because it wraps right around them, and its width is the height of the cylinder.

What does the net of a square-based pyramid consist of?

One square for the base and four congruent triangles for the sloping faces. The perpendicular height of each triangle is the slant height of the pyramid, not its vertical height.

IGCSEMathsCambridge (CIE)CoreFlashcardsGeometrySymmetry & Shapes

Symmetry & Shapes (Cambridge (CIE) IGCSE Maths: Core): Flashcards

Exam code: 0580 & 0980

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FrontIntroduction to Lines & Angles
Define a line segment.

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Cards in this collection (39)

Define a line segment.
A line segment is the part of a line between two end points, unlike a line itself, which carries on forever in both directions.
A segment starting at $A$ and ending at $B$ is written as $A B$ .
On a diagram, what do arrows drawn on two lines mean, and what do tick marks mean?
Arrows show that the lines are parallel; tick marks show that the lines are equal in length.
Where a diagram has a second, separate pair of each, double arrows and double ticks are used to keep the two pairs apart.
What does it mean for two lines to be perpendicular?
They intersect at right angles, meaning the angle between them is 90°.
On a diagram this is marked with a small square at the point where they cross.
Complete the two descriptions by filling in the missing names:
An angle smaller than 90° is called an $______$ angle.
An angle between 90° and 180° is called an $______$ angle.
The completed descriptions are:
An angle smaller than 90° is called an acute angle.
An angle between 90° and 180° is called an obtuse angle.
True or False?
An angle of 200° is called a reflex angle.
True.
Any angle greater than 180° but less than 360° is reflex.
An angle of exactly 180° is a straight angle, so reflex angles pick up where that leaves off.
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.
Complete the polygon names by filling in the missing words:
A polygon with $5$ sides is a $______$ .
A polygon with $7$ sides is a $______$ .
A polygon with $9$ sides is a $______$ .
The completed names are:
A polygon with $5$ sides is a pentagon.
A polygon with $7$ sides is a heptagon.
A polygon with $9$ sides is a nonagon.
Complete the triangle names by filling in the missing words:
An $______$ triangle has three sides of equal length.
An $______$ triangle has two sides of equal length.
A $______$ triangle has no sides of equal length.
The completed names are:
An equilateral triangle has three sides of equal length.
An isosceles triangle has two sides of equal length.
A scalene triangle has no sides of equal length.
A square is a special kind of rectangle, and a rhombus is a special kind of parallelogram. What do both special cases have in common?
In each case, all four sides are the same length.
A rectangle and a parallelogram each have two pairs of equal sides; making all four equal is what produces the square and the rhombus.
A quadrilateral has exactly one pair of parallel sides. What is it called, and what is it called if it has two pairs?
One pair of parallel sides makes it a trapezium.
Two pairs of parallel sides make it a parallelogram.
How are the equal sides of a kite arranged, compared with those of a parallelogram?
A kite's equal sides are adjacent, meaning next to each other, in two pairs.
A parallelogram's equal sides are opposite each other, and unlike a parallelogram a kite has no parallel sides at all.
What does it mean to say that a diagonal bisects another?
It cuts the other diagonal exactly in half, crossing it at its midpoint.
In a square, rectangle, parallelogram and rhombus each diagonal bisects the other; in a trapezium neither does.
In which quadrilaterals are the two diagonals perpendicular?
In the square, the rhombus and the kite.
In a rectangle, a parallelogram and a trapezium the diagonals cross at some other angle.
True or False?
The two diagonals of a kite bisect each other.
False.
Only one of a kite's diagonals bisects the other.
The longer diagonal cuts the shorter one in half, but the shorter one does not return the favour.
Define a chord of a circle.
A chord is a straight line joining two points on the circumference.
It does not have to pass through the centre, and it does not extend beyond the circle.
Define a segment of a circle.
A segment is the region enclosed between a chord and the arc that the chord cuts off.
Every chord creates two segments, a larger one and a smaller one.
Define a tangent to a circle.
A tangent is a straight line that touches the circumference at exactly one point.
Unlike a chord, it does not cut across the circle at all.
True or False?
Every diameter is also a chord.
True.
A diameter joins two points on the circumference, which is exactly what a chord does.
A diameter is simply the special chord that passes through the centre, and it is the longest chord a circle has.
Why is a diameter a line of symmetry of a circle?
Because it passes through the centre, so it splits the circle into two identical halves.
A circle has infinitely many lines of symmetry, since every diameter is one.
Define a prism.
A prism is a 3D shape with the same cross-section all the way through its length.
The cross-section of a cube is a square, and that of a cuboid is a rectangle.
Complete the three descriptions by filling in the missing words:
A $______$ is a single surface of a 3D shape.
A $______$ is a corner of a 3D shape.
An $______$ joins one corner to another.
The completed descriptions are:
A face is a single surface of a 3D shape.
A vertex is a corner of a 3D shape.
An edge joins one corner to another.
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 counts, because it is a cube with its square faces stretched into rectangles.
How many faces, edges and vertices does a triangular prism have?
A triangular prism has $5$ faces, $9$ edges and $6$ vertices.
The faces are the two triangular ends and the three rectangles joining them.
What is a tetrahedron?
A tetrahedron is a triangular-based pyramid.
It has $4$ triangular faces, one for the base and three sloping up to meet at a point.
Why is a cylinder described as being similar to a prism?
Because it also has the same cross-section all the way through, in its case a circle.
Its two circular ends are identical, exactly as a prism's two ends are.
True or False?
The three rectangular faces of a triangular prism are always equal to one another.
False.
All three are equal only when the triangular ends are equilateral.
If the triangular ends are isosceles then only two of the rectangles match, because the rectangles take their widths from the sides of the triangle.
Define the net of a solid.
A net is a 2D drawing that can be cut out and folded up to make the 3D shape.
Each face of the solid appears once in the net, arranged so that the right edges meet when it is folded.
How is the area of a net related to the solid it folds into?
The area of the net is exactly the surface area of the solid.
Folding does not change how much material there is, it only rearranges it in space.
True or False?
Any arrangement of six squares joined edge to edge will fold up into a cube.
False.
Only 11 different arrangements of six squares actually fold into a cube.
A solid can have more than one net, but not every arrangement of the right faces is one.
What shapes make up the net of a cylinder, and what are the rectangle's dimensions equal to?
Two circles and one rectangle.
The rectangle's length is the circumference of the circles, because it wraps right around them, and its width is the height of the cylinder.
What does the net of a square-based pyramid consist of?
One square for the base and four congruent triangles for the sloping faces.
The perpendicular height of each triangle is the slant height of the pyramid, not its vertical height.
Complete the description of the net of a cuboid by filling in the missing numbers:
The net of a cuboid is made from $______$ rectangles, which come in $______$ matching pairs.
The completed description is:
The net of a cuboid is made from $6$ rectangles, which come in $3$ matching pairs.
Opposite faces of a cuboid are identical, which is what pairs them up.

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