GEOMETRY ---- BASIC MATHEMATICS-----THE UNITED REPUBLIC OF TANZANIA.

GEOMETRY-- BASIC   MATHEMATICS.

 

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)

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
• Shapes Freeplay

• Perimeter

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

• General Drawing Tool

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 Sector and Segment
• Circle Area by Sectors
• Annulus
• Activity: Dropping a Coin onto a Grid

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

Acute Angles

Right Angles

Obtuse Angles

Straight Angle

Reflex Angles

Full Rotation

Degrees (Angle) Radians Congruent Angles Parallel Lines and Pairs of Angles Transversal A Triangle Has 180° Supplementary Angles Complementary Angles

Angles Around a Point Angles on a Straight Line Interior Angles Exterior Angles Interior Angles of Polygons Exterior Angles of Polygons

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
• Ellipse
• Parabola
• Hyperbola

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: (if any surface is not flat)	Sphere Torus Cylinder Cone

• Polyhedron Models
• Vertices, Faces, and Edges
• Euler's Theorem