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 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.

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:

Pentagon

Pentagram

Hexagon

• 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

Using Drafting Tools

• Geometric Constructions
• 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 and Projectile Animation
• Hyperbola

Circle Theorems

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

Triangle Centers

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):

	Cubes and Cuboids (Volume of a Cuboid)
	Platonic Solids
	Prisms
	Pyramids

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

	Sphere			Torus
	Cylinder			Cone

• Polyhedron Models
• Volume and Area of a Sphere Calculator
• Spheroid
• Cross Sections
• Vertices, Faces, and Edges
• Cone vs Sphere vs Cylinder
• Pyramid vs Cone
• Prism vs Cylinder
• Pyramid vs Cube
• Volume of Horizontal Cylinder
• Euler's Theorem
• Pythagoras in 3D
• Hypercubes
• Builder's Math
• Moments of Area