See below if this confuses you!
Square
Squares have 4 equal sides and 4 right angles.
They have 4 lines of symmetry.
All squares belong to the rectangle family.
All squares belong to the rhombus family.
All squares are also parallelograms.
Rectangle
Rectangles have 4 sides and 4 right angles.
They all have 2 lines of symmetry (4 lines if they are also a
square!)
All rectangles belong to the parallelogram family.
Rhombus Rhombuses (rhombii) have 4 equal sides.
Both pairs of opposite sides are parallel.
They all have 2 lines of symmetry (4 lines if they are a
square!)
All rhombuses belong to the parallelogram family.
Parallelogram
Parallelograms have 2 pairs of parallel sides.
Some parallelograms have lines of symmetry (depending on
whether they are also squares, rectangles or rhombuses),
but most do not.
Trapezoids US (Trapeziums UK) have one pair of parallel
sides.
Trapezoid US
Some trapezoids have a line of symmetry.
(Trapezium UK)
Please note the differences between the definitions for US
and UK.
Kite
Kites have 2 pairs of equal sides which are adjacent to each
other.
Trapezium US
(Trapezoid UK)
Trapeziums US (Trapezoids UK) are quadrilaterals with no
parallel sides.
Please note the differences between the definitions for US
and UK.
Regular and Irregular Polygons
Equilateral Triangle Irregular Triangle
Angle: 60°
Interior angles add up to 180°
Square Irregular Quadrilateral
Angle: 90°
Interior angles add up to 360°
Pentagon Irregular Pentagon
Angle: 108°
Interior angles add up to 540°
Hexagon Irregular Hexagon
Angle: 120°
Interior angles add up to 720°
Heptagon Irregular Heptagon
Angle: 128.6°
Interior angles add up to 900°
Octagon Irregular Octagon
Angle: 135°
Interior angles add up to 1080°
Nonagon Irregular Nonagon
Angle: 140°
Interior angles add up to 1260°
Decagon
Angle: 144°
Interior angles add up to 1440°
Circle
Circles have a point in the centre from which
each point on the diameter is equidistant.
They have infinite lines of symmetry.
How many sides does a circle have?
This is an interesting question - the answer could
be 0 (no straight sides), 1 curved side, or an
infinite number of sides are all possibleanswers.
Ellipse Ellipses are like circles which have been squashed
or stretched.
They have 2 lines of symmetry.
They are also a special type of oval.
The longest and shortest diameters of the ellipse
are called the major and minor axes.
These axes are also the lines of symmetry.
Crescent Crescent shapes are made when two circles
overlap, or when one circle is removed from
another circle .
The perimeter of crescents are made from two
circular arcs.
They have 1 line of symmetry.
Our moon forms crescent shapes during its
phases.
Some countries such as Turkey or Algeria have
crescent shapes on their flags.
List of Geometrics Shapes - 3D Shapes
Here are some common 3D shapes that you should know.
Along with a picture of each shape, the number of faces, edges and vertices are also given.
Common properties of the 3D shapes are also given.
Please note that there is some disagreement over the definitions and properties of 3d shapes.
Some mathematicians allow a face to be curved and some do not.
Some mathematicians allow an edge to be curved and some do not.
Cube
Cubes have 6 faces, 12 edges and 8 vertices.
All sides on a cube are equal length.
All faces are square in shape.
A cube is a type of cuboid.
Cuboid
Cuboids have 6 faces, 12 edges and 8 vertices.
All the faces on a cuboid are rectangular.
Sphere
Spheres have either 0 or 1 faces, 0 edges and 0 vertices.
Cylinder
Cylinders have either 2 or 3 faces, 0 or 2 edges, and 0
vertices.
Cone
Cones have either 1 or 2 faces, 0 or 1 edges, and 1 apex
(which is described by some mathematicians as a vertex).
Triangular Prism
Triangular Prisms have 5 faces, 9 edges, and 6 vertices.
The two faces at either end are triangles, and the rest of the
faces are rectangular.
Hexagonal Prism
Hexagonal Prisms have 8 faces, 18 edges, and 12 vertices.
The two faces at either end are hexagons, and the rest of
the faces are rectangular.
Triangular-based Pyramid
Triangular-based pyramids have 4 faces, 6 edges and 4
vertices.
The base is a triangle. All of the faces are triangular.
If the triangular faces making up the prism are all
equilateral, then the shape is also called a Tetrahedron.
Square-based Pyramid Square based pyramids have 5 faces, 8 edges and 5 vertices
The base is a square. All the other faces are triangular.
Hexagonal Pyramid
Hexagonal pyramids have 7 faces, 12 edges, and 7 vertices.
The base is a hexagon. All of the other faces are triangular.
The 5 Platonic Solids
The platonic solids form a set of 5 polyhedra with the following special properties:
the faces of the platonic solids have to be regular and congruent.
the same number of faces meet at each vertex.
They are named after the Greek philosopher Plato who wrote about them in his philosophical
discussions.
There are only 5 platonic solids:
Regular tetrahedron
Cube or regular hexahedron
Regular octahedron
Regular dodecahedron
Regular icosahedron
Tetrahedron A Tetrahedrons is the same as a triangular pyramid.
They have 4 triangular faces, 6 edges and 4 vertices.
A regular tetrahedron has equilateral triangles for its faces,
and is one of the 5 platonic solids.
Cube (regular hexahedron) Cubes have 6 faces, 12 edges and 8 vertices.
All sides on a cube are equal length.
All faces are square in shape.
A cube is a type of cuboid and is one of the 5 platonic
solids.
Octahedron
Octahedrons are a shape with 8 faces, 12 edges and 6
vertices.
A regular octahedron has equilateral triangles for its faces,
and is one of the 5 platonic solids.
Dodecahedron
Dodecahedrons are a shape with 12 faces, 30 edges and 20
vertices.
A regular dodecahedron has regular pentagons for its faces,
and is one of the 5 platonic solids.
Icosahedron Icosahedron are a shape with 20 faces, 30 edges and 12
vertices.
All the faces are triangles.
A regular icosahedron is one of the 5 platonic solids with all
faces being equilateral triangles.
