Geometry

2D Shapes

Regular Polygons

A polygon is a plane (2D) shape with straight sides.
To be a regular polygon all the sides and angles must be the same:

Triangle - 3 Sides	Square - 4 Sides
Pentagon - 5 Sides	Hexagon - 6 sides
Heptagon - 7 Sides	Octagon - 8 Sides
Nonagon - 9 Sides	Decagon - 10 Sides
More ...

Other Common Polygons

Quadrilateral Any 4 sided 2D shape	Rectangle - 4 Sides All right angles
And many more!

Curved Shapes

These 2D shapes have curves, so are not polygons:

Circle	Ellipse
And many more!

Solid Geometry

Solid Geometry is the geometry of three-dimensional space, the kind of space we live in ...

Three Dimensions

It is called three-dimensional, or3D because there are threedimensions: width, depth andheight.

Simple Shapes

Let us start with some of the simplest shapes:

Common 3D Shapes

Properties

Solids have properties (special things about them), such as:

• volume (think of how much water it could hold)
• surface area (think of the area you would have to paint)
• how many vertices (corner points), faces and edges they have

Polyhedra and Non-Polyhedra

There are two main types of solids, "Polyhedra", and "Non-Polyhedra":

Polyhedra : (they must have flat faces)	Cubes and Cuboids (Volume of a Cuboid)      Platonic Solids    Prisms    Pyramids
Non-Polyhedra: (if any surface is not flat)	Sphere Torus Cylinder Cone

Perpendicular and Parallel

Perpendicular

It just means at right angles (90°) to.

The red line is perpendicular to the blue line in both these cases:

(The little box drawn in the corner, means "at right angles", so we didn't really need to also show that it was 90°, but we just wanted to!)

Try for yourself:

Parallel

Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. (They also point in the same direction). Just remember:

Always the same distance apart and never touching.

The red line and blue line are parallel in both these examples:

Example 1		Example 2

Try it yourself:

Perpendicular to Parallel

Question: What is the difference between perpendicular and parallel? 
Answer: 90 degrees (a right angle)

That's right, when we rotate a perpendicular line by 90° it becomes parallel (but not if it touches!)

Perpendicular ...	Rotate One Line 90°	... Parallel !

Likewise, parallel lines become perpendicular when one line is rotated 90°.

Parallel Curves

Curves can also be parallel when they are always the same distance apart (called "equidistant"), and never meet. Just like railroad tracks.

The red curve is parallel to the blue curve in both these cases:

Parallel Surfaces

Surfaces can also be parallel, so long as the rule still holds: always the same distance apart and never touching.