Sunday, July 5, 2015

Geometry

GeometryGeometry 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: 

planePlane Geometry is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper
  
Solid Geometry is about three dimensional objects like cubes, prisms, cylinders and spheres.

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

dimensions

Point, Line, Plane and Solid

Point has no dimensions, only position
Line is one-dimensional
Plane is two dimensional (2D)
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).




Polygons

Polygon is a 2-dimensional shape made of straight lines. Triangles and Rectangles are polygons.
Here are some more:


The Circle

Circle Theorems (Advanced Topic)

Symbols

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

Congruent and Similar


Angles


Compass 

Using Drafting Tools


Transformations and Symmetry

symmetry drawing



Coordinates

interactive-cartesian-coordinates


More Advanced Topics in Plane Geometry

Pythagoras

abc triangle

Conic Sections


Trigonometry

Right-Angled Triangle
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:

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
  
Non-Polyhedra:
(if any surface is not flat)
sphereSpheretorusTorus
cylinderCylinderconeCone

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