Geometry

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

Geometry can be divided into:

**Plane 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.

## Point, Line, Plane and Solid

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).

* 2D Shapes
* Activity: Sorting Shapes
* Triangles
* Right Angled Triangles
* Interactive Triangles

* Quadrilaterals (Rhombus, Parallelogram, etc)
* Rectangle, Rhombus, Square, Parallelogram, Trapezoid and Kite
* Interactive Quadrilaterals
* Parallelogram In Any Quadrilateral
* Paper Sizes
* Shapes Freeplay

* Perimeter

* Area
* Area of Plane Shapes
* Area Calculation Tool
* Area of Polygon by Drawing
* Activity: Garden Area

* General Drawing Tool
* Square Calculator and Rectangle Calculator

### Polygons

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

Here are some more:

* Properties of Regular Polygons
* Diagonals of Polygons
* Interactive Polygons

### The Circle

* Circle
* Pi
* Circle Area by Lines
* Circle Sector and Segment
* Circle Area by Sectors
* Activity: Dropping a Coin onto a Grid
* Arc
* Annulus

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

* Congruent Shapes
* Similar Shapes

### Angles

Types of Angles

* Radians

* Congruent Angles
* Parallel Lines and Pairs of Angles
* Transversal
* Adjacent Angles
* A Triangle Has 180°

* Supplementary Angles
* Complementary Angles
* Angles on a Straight Line

* Interior Angles
* Exterior Angles

* Interior Angles of Polygons
* Exterior Angles of Polygons

* Using the Protractor
* Using the Drafting Triangle and Ruler
* Using a Ruler and Compass

### Transformations and Symmetry

Transformations:

* Rotation
* Reflection
* Translation
* Resizing

Symmetry:

* Reflection Symmetry
* Rotational Symmetry
* Point Symmetry
* Lines of Symmetry of Plane Shapes

* Symmetry Artist

* Activity: Symmetry of Shapes
* Activity: Make a Mandala
* Activity: Coloring (The Four Color Theorem)

* Tessellations
* Tessellation Artist

### Coordinates

* Cartesian Coordinates
* Interactive Cartesian Coordinates
* Hit the Coordinate Game

## More Advanced Topics in Plane Geometry

### Pythagoras

* Pythagoras' Theorem
* Pythagorean Triples

### Conic Sections

* Set of all points
* Conic Sections
* Eccentricity
* Ellipse
* Parabola
* Hyperbola

### Circle Theorems

* Circle Theorems
* Tangent and Secant Lines
* Intersecting Secants Theorem
* Intersecting Chords Theorem
* Angle of Intersecting Secants Theorem

## Trigonometry

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

* Introduction to Trigonometry
* Trigonometry Index

## 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:

Common 3D Shapes

### Polyhedra and Non-Polyhedra

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

Polyhedra *(they must have flat faces)*:

Cuboids(Volume

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

* Polyhedron Models
* Volume and Area of a Sphere Calculator
* Cross Sections
* Triangle Centers
* Vertices, Faces, and Edges
* Cone vs Sphere vs Cylinder
* Pyramid vs Cone
* Prism vs Cylinder
* Volume of Horizontal Cylinder
* Euler's Theorem
* Pythagoras in 3D