2D Geometry
To see the working of geometry is to see the design of nature. To understand the makeup of geometry, we must first know how it is constructed. Every shape you can think of is made from a series of points. Points make lines, lines make planes and planes make objects. Every object in the universe can be located by its points but we must first know where to begin.
Geometry is the mathematical study of shapes, figures and positions in space. Basic shapes are the line, the circle, the triangle, and the square. The point is the smallest unit of geometry. It takes three parts to make a line segment: a beginning, middle and end. A circle is a series of all points in a plane at a fixed distance (radius) from the center point. Planes have length (x) and height (y). Objects in space are things like points, lines, and angles. Perpendicular lines are lines or line segments that intersect or meet at 90 degrees. A ray is a line with one fixed point and one directional arrow.
Remember  plane geometry is two dimensional but we live in a three dimensional world!
Activity 1 Magic of the Point and Line
Geometry orders our universe, but we first need to be able to recognize it. We measure geometry with a compass and a line. Place two points horizontal from each other and draw a line between them. Take your compass and draw two arcs with their centers on each of your two end points (be certain that the arc is larger than half the distance between the two points). The arcs will cross each other. Next, draw a line, it should be vertical, to connect the two points where the arcs meet. You now have divided your original line in half. You can use this method to not only divide a line into two but also to draw a perfect square or rectangle. Can you figure out how?
Activity 2 Find the Origin and Divide the World
You need a pencil, a straight edge, a compass and a hard flat surface. Begin by drawing a line, straight and simple. Pick a point on that line, anywhere. This is now your origin. Use your compass to draw a circle around your origin. Put the point of your compass on the origin and expand the compass outward. Keeping the point on the origin, rotate the compass 360 degrees. Next, draw two lines, one horizontal, one vertical, from your point of origin to the outside edge of the circle. You have just divided the circle into four quadrants. Finally, connect the outside points of your line to form a square around the circle and draw a diagonal line from the four corners to the opposite corner and then again to the opposite end of your original vertical line. You should see a square with a circle around it, a cross through the middle, with an X and a V in the center. From this diagram, you can find the angles to divide any circle into equal parts from one to ten.
Activity 3 Design Your Own Geometry
Divide a piece of paper into four quadrants with a vertical line and a horizontal line. Place nine dots in three lines of three dots, in each quadrant; you will have 36 dots total, in a regular pattern. Next, draw your own polygons. Draw some with three sides, five sides or even ten sides. Draw some regular polygons (a closed shape with equal sides), irregular polygons (a closed shape with unequal sides), concave shapes (a dented shape) and convex shapes (a shape with a bulge). Then, label each shape with a number. Create a key along one side of your paper to test your friends. Test each other; see how many shapes they can name!
Activity 4 Geometry of Constellations
Geometry orders our universe, but we must first be able to recognize it. We measure geometry with a compass and a line. People who came before us connected the stars above into geometric constellations. InvestigateYour Skyand click on the city where you live. Download a map of the night sky above your home. Be sure to uncheck the Constellation Display option so you can create your own patterns. Print your overhead star map and use your pencil and a straight edge to connect the brightest stars. What sort of images do you see? An animal? Some sort of vehicle? A person? Write your name in the stars. Claim a piece of sky for yourself! Be sure to label your constellations so others can find the images you have discovered.
Review

The smallest geometric unit is:

Perpendicular lines are lines that meet at a right angle (90 degrees).

Lines have a beginning point, a middle point and an end point.

Lines are always straight.

Lines can never intersect.
Explore
 Geometry of the Circle
 Elements of Geometry
 Geometric Shapes
 Geometry is FUN!
 The Dot and the Line: A Romance in Lower Mathematics Video
 Geometry of the Circle by Philip Glass
 Exploring Other Dimensions
 Bisecting Lines and Angles
 Geometry Worksheets
 Geometry From the Land of the Incas
 Geometric Patterns in Islamic Art
 Sacred Geometry
 Angles Concentration
 Measuring Angles
 Perimeter and Area Spaceship
 Pi World or 3.14
 Look Up into the Night Sky
 Neave Planetarium
 Waldorf Circle Multiplication
Relate
 Composition
 Line
 Shape
 Stairs
 Object Description
 Measure
 Proportion
 De Stijl
 Architecture
 Self Portrait
 Animation
 Metrics
 Form
 Area
 3D Geometry
 Origami
 Architectonics
 Pattern
 Prairie Architecture
 Categories
 Photography
 Textiles
 Frames
 Digital Modeling
 Numbers
 Habitat
 Space
 symmetry
 Volume
 Paper Airplanes
 Film+Video
 Paper Engineering
 Aeronautics
 Sound
 Pavilions
 Money
 City
 Wayfinding
 Magazines