UNDERSTANDING SHAPES

Equilateral Triangle	Equilateral triangles have all angles equal to 60°, and all sides equal length. All equilateral triangles have 3 lines of symmetry.
Isoscles Triangle	Isosceles triangles have 2 angles equal and 2 sides of equal length. All isosceles triangles have a line of symmetry.
Scalene Triangle	Scalene triangles have no angles equal, and no sides of equal length.
Right Triangle	Right triangles (or right angled triangles) have one right angle (equal to 90°).
Obtuse Triangle	Obtuse triangles have one obtuse angle (an angle greater than 90°). The other two angles are acute (less than 90°).
Acute Triangle	Acute triangles have all angles acute.

List of Geometric Shapes - Quadrilaterals

A quadrilateral is a polygon with 4 sides.

There are quite a few members of the quadrilateral family. There are also some members which are a subset of other members of this family!
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.
Trapezoid US (Trapezium UK)	Trapezoids US (Trapeziums UK) have one pair of parallel sides. Some trapezoids have a line of symmetry. 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

Here is a list of regular polygons from 3 to 10 sides.

For each polygon, a regular and an irregular example have been shown.

Any regular shape will be mathematically similar to the example shown (having the same angles).

There are an infinite number of examples of different irregular polygons that could be shown, and only one example is given.

Equilateral Triangle Angle: 60° Interior angles add up to 180°	Irregular Triangle
Square Angle: 90° Interior angles add up to 360°	Irregular Quadrilateral
Pentagon Angle: 108° Interior angles add up to 540°	Irregular Pentagon
Hexagon Angle: 120° Interior angles add up to 720°	Irregular Hexagon
Heptagon Angle: 128.6° Interior angles add up to 900°	Irregular Heptagon
Octagon Angle: 135° Interior angles add up to 1080°	Irregular Octagon
Nonagon Angle: 140° Interior angles add up to 1260°	Irregular Nonagon
Decagon Angle: 144° Interior angles add up to 1440°	Irregular Decagon

The formulae for the interior angles of a polygon are as follows: 

Total of interior angles = 180 x (number of sides - 2)

Angle = total of interior angles / number of sides

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.