Symmetry & Shapes Flashcards

All 35 cards in this deck

What is meant by the order of rotational symmetry of a shape?

The number of times the shape fits exactly onto itself during one full turn ($360°$).

What is the order of rotational symmetry of a regular polygon with $n$ sides?

e.g. a regular hexagon

$n$.

A regular hexagon has order $6$.

True or false? A shape with no rotational symmetry has rotational symmetry of order $0$.

False. It has order $1$, because every shape fits onto itself after a full turn.

What is the order of rotational symmetry of a rectangle that is not a square?

$2$.

For a shape with rotational symmetry of order $n$, what is the smallest angle of rotation that maps it onto itself?

e.g. order $5$

$360° \div n$.

Order $5$ gives $72°$.

What are the steps to find the order of rotational symmetry of a shape?

e.g. an equilateral triangle

1. Mark the centre of the shape.
2. Turn the shape through one full turn, counting each position where it looks exactly the same: $3$ positions.
3. That count is the order: order $3$.

What is a line of symmetry of a 2D shape?

A mirror line: folding along it makes the two halves fit exactly onto each other.

How many lines of symmetry does a regular polygon with $n$ sides have?

e.g. a regular pentagon

$n$.

A regular pentagon has $5$ lines of symmetry.

How many lines of symmetry does a rhombus have, and where are they?

$2$ — along its two diagonals.

True or false? A parallelogram has two lines of symmetry.

False. A parallelogram (not a rectangle or rhombus) has no lines of symmetry, only rotational symmetry of order $2$.

How many lines of symmetry does an isosceles trapezium have?

$1$ — the line through the midpoints of the two parallel sides.

What does a line of symmetry of a polygon tell you about its sides and angles?

e.g. a kite

Sides and angles that reflect onto each other are equal.

In a kite the two angles either side of the line of symmetry are equal, so an unknown one can be deduced.

What is a plane of symmetry of a 3D solid?

A flat surface that cuts the solid into two halves, each one a mirror image of the other.

How many planes of symmetry does a cube have?

$9$ — $3$ parallel to pairs of faces and $6$ through pairs of opposite edges.

How many planes of symmetry does a cuboid with three different edge lengths have?

$3$ — one halfway through each pair of opposite faces.

How many planes of symmetry does a cylinder have?

Infinitely many — every vertical plane through its axis, plus the horizontal plane halfway up.

True or false? A prism whose cross-section is an equilateral triangle has $4$ planes of symmetry.

True. Three planes along the length (one through each vertex of the triangle) and one halfway along the length.

What is a trapezium?

A quadrilateral with exactly one pair of parallel sides.

Which quadrilateral has two pairs of equal adjacent sides, one line of symmetry and diagonals that meet at right angles?

A kite.

What are the properties of the diagonals of a rhombus?

They bisect each other at right angles and bisect the angles of the rhombus.

What is true of the opposite sides and opposite angles of a parallelogram?

Opposite sides are equal and parallel; opposite angles are equal.

True or false? Every rhombus is a square.

False. Every square is a rhombus, but a rhombus need not have right angles.

In a geometric diagram, what do matching dashes on two sides, and matching arrows on two sides, mean?

Matching dashes mean the sides are equal in length; matching arrows mean the sides are parallel.

How many faces, edges and vertices does a cube have?

$6$ faces, $12$ edges, $8$ vertices.

What is a prism?

A solid with the same cross-section all along its length, with two identical parallel end faces.

How many faces, edges and vertices does a square-based pyramid have?

$5$ faces, $8$ edges, $5$ vertices.

How many faces, edges and vertices does a cylinder have?

$2$ flat faces and $1$ curved surface, $2$ edges, $0$ vertices.

How many faces, edges and vertices does a cone have?

$1$ flat face and $1$ curved surface, $1$ edge, $1$ vertex (the apex).

True or false? A sphere has one face and one edge.

False. A sphere has one curved surface, no edges and no vertices.

What is the plan of a 3D solid?

The view of the solid looking down on it from directly above.

What is the front elevation of a 3D solid?

The view of the solid looking at it horizontally from the front.

What is the side elevation of a 3D solid?

The view looking at the solid horizontally from the side, at right angles to the front elevation.

True or false? The plan of a cylinder standing on its circular base is a rectangle.

False. The plan is a circle; the elevations are rectangles.

What are the steps to draw the plan and elevations of a solid on a grid?

e.g. a cuboid $3$ wide, $2$ deep and $5$ high

1. Plan: draw the view from above, a rectangle $3$ wide and $2$ deep.
2. Front elevation: draw the view from the front, $5$ high and $3$ wide.
3. Side elevation: draw the view from the side, $5$ high and $2$ wide.

A solid has a circular plan, and its front and side elevations are both identical triangles. What is the solid?

A cone.