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 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)
0 1 2 3
Dimensions
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
acute right obtuse straight reflex full
rotation
Acute Angles Right Angles Obtuse Angles Straight Angle Reflex Angles Full Rotation
Degrees (Angle)
Radians
Angles Around a Point
Angles on a Straight Line
Congruent Angles
Parallel Lines and Pairs of Angles
Interior Angles
Transversal
Exterior Angles
Adjacent Angles
Interior Angles of Polygons
A Triangle Has 180°
Exterior Angles of Polygons
Supplementary Angles
Complementary 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
c
Pythagorean Triples
a
Conic Sections
Set of all points
Conic Sections
Eccentricity
Ellipse
Parabola
Hyperbola
Circle Theorems t
gen
n t
Ta can
Circle Theorems Se rd
Cho
t er
Tangent and Secant Lines Diame
Ra
Intersecting Secants Theorem diu
s
Ar
Intersecting Chords Theorem c
Angle of Intersecting Secants Theorem
Trigonometry
Trigonometry is a special subject of its own, so you
e
might like to visit:
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pote
Introduction to Trigonometry H y
Opposite
Trigonometry Index θ
Adjacent
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
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
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