2D Shapes

Regular Polygons
polygon is a plane (2D) shape with straight sides.
To be a regular polygon all the sides and angles must be the same:
2d triangle
Triangle - 3 Sides
2d square
Square - 4 Sides
2d pentagon
Pentagon - 5 Sides
2d hexagon
Hexagon - 6 sides
2d heptagon
Heptagon - 7 Sides
2d octagon
Octagon - 8 Sides
2d nonagon
Nonagon - 9 Sides
2d decagon
Decagon - 10 Sides
More ...

Other Common Polygons
2d quadrilateral
Any 4 sided 2D shape
2d rectangle
Rectangle - 4 Sides
All right angles
And many more!

Curved Shapes
These 2D shapes have curves, so are not polygons:
2d circle
2d 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 threedimensionswidth, depth andheight.

Simple Shapes

Let us start with some of the simplest shapes:


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

Polyhedra and Non-Polyhedra

There are two main types of solids, "Polyhedra", and "Non-Polyhedra":
Polyhedra :
(they must have flat faces)
hexahedron square prismCubes and
Cuboids (Volume
of a Cuboid
tetrahedron hexahedron octahedron dodecahedorn icosahedronPlatonic Solids
triangular prism square prism pentagonal prismPrisms
triangular pyramid square pyramid pentagonal pyramidPyramids
(if any surface is not flat)

Perpendicular and Parallel


It just means at right angles (90°) to.
The red line is perpendicular to the blue line in both these cases:
Perpendicular Example 1Perpendicular Example 2
(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:


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:
Parallel Example 1Parallel Example 2
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!)
PerpendicularRotate 90 Degrees

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 Curves Example 1Parallel Curves Example 1

Parallel Surfaces

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

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