Geometry

Geometry is all about shapes and their properties.

If you like playing with objects, or like drawing, then geometry is for you!

Geometry can be divided into:

plane


Plane Geometry is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper

 

3d shapes


Solid Geometry is about three dimensional objects like cubes, prisms, cylinders and spheres.

right arrowHint: Try drawing some of the shapes and angles as you learn ... it helps.

Point, Line, Plane and Solid

dimensions

A Point has no dimensions, only position
A Line is one-dimensional
A Plane is two dimensional (2D)
A Solid is three-dimensional (3D)

Why?

Why do we do Geometry? To discover patterns, find areas, volumes, lengths and angles, and better understand the world around us.

Plane Geometry

Plane Geometry is all about shapes on a flat surface (like on an endless piece of paper).

Regular Pentagon

 

rectangle




Polygons

A Polygon is a 2-dimensional shape made of straight lines. Triangles and Rectangles are polygons.

Here are some more:

PentagonPentagon
PentagramPentagram
HexagonHexagon

 

 

The Circle

pi circle diameter

Circle Theorems (Advanced Topic)

 

Symbols

There are many special symbols used in Geometry. Here is a short reference for you:

Geometric Symbols

 

Congruent and Similar

 

Angles

Types of Angles
angles

Acute AnglesRight AnglesObtuse AnglesStraight AngleReflex AnglesFull Rotation





 

Compass 

Using Drafting Tools

protractor

 

Transformations and Symmetry

Transformations:

symmetry drawing

Symmetry:



Activity


 

Coordinates

interactive-cartesian-coordinates

 

 

More Advanced Topics in Plane Geometry

Pythagoras

abc triangle

 

Conic Sections

ellipse draw 3

 

circle lines

Circle Theorems

Triangle Centers

Trigonometry

triangle showing Opposite, Adjacent and Hypotenuse

Trigonometry is a special subject of its own, so you might like to visit:

 

Solid Geometry

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

... let us start with some of the simplest shapes:

shapes thumbnail
Common 3D Shapes

Polyhedra and Non-Polyhedra

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

Polyhedra (they must have flat faces):

cube or hexahedron square prismCubes and
Cuboids (Volume
of a Cuboid
)
tetrahedron cube or hexahedron octahedron dodecahedron icosahedronPlatonic Solids
triangular prism square prism pentagonal prismPrisms
triangular pyramid square pyramid pentagonal pyramidPyramids

Non-Polyhedra (when any surface is not flat):

sphereSphere torusTorus
cylinderCylinder coneCone