LINKS TO GEOGEBRA FILES

On this site at present there are GeoGebra demonstration files for the following areas of study:

GEOMETRY – TRIGONOMETRY – DIFFERENTIATION – ALGEBRA – MEASURE – GRAPH DRAWING – COORDINATE GEOMETRY

 

 

Geometry

Section 1

1.  Naming Points and Lines

 

2.  Naming Triangles, Angles

 

3.  Parts of an Angle – Arms, Vertex, Degree measure

 

4. Construct Perpendicular lines, Measure Length

 

5.  Review Axial Symmetry

 

6.  Review Central Symmetry

 

7.  Review Translations

 

Section 2

1.  See a Split Straight Angle

 

2. See Vertically Opposite Angles are Equal in Measure

 

3. Use Paper-folding methods to see that the Three Interior Angles of a Triangle Add to 180°

 

4. See an Isosceles Triangle has Two Equal Sides and Two Equal Angles

 

5. See an Equilateral Triangle has Three Equal Sides and Three Equal Angles, each 60oo

Section 3

Symmetries

1. See how an Axial Symmetry requires Perpendicular lines in its construction

 

2. See how a Central Symmetry requires Lines through a Point in its construction

 

3. See the Images of Coloured Squares under Central Symmetry

 

4. See a Translation as a Wallpaper Pattern

 

5. Find the Image of a Triangle under a Translation

 

Section 4

Constructions -1

 

1. Construct the Perpendicular Bisector of a Line Segment

 

2. Construct the Bisector of an Angle

 

3. Construct the Trisection of a Line Segment

Section 5

Constructions –2

 

1. Construct a Triangle given 3 Side Lengths – SSS

 

2. Construct a Triangle given 2 Angles and the Side Included between them – ASA

 

3. Construct a Triangle given 2 Sides and the Angle Included between them – SAS

 

4. Construct a Triangle given a Right Angle, a Hypotenuse and another Side – SS90 (RHS)

           

Section 6

Circles – Angles

 

1. See the Angle in a Semicircle is 90 degrees

 

2. See a Tangent Line makes an Angle of 90 degrees with a Diameter Line

 

3. See Opposite Angles in a Cyclic Quadrilateral Sum to 180 degrees

Section 7

Using Geogebra files to examine the Theorem of Pythagoras

 

1: Showing Squares on each side of a Triangle.  Showing full results for Area and Lengths of sides.

 

2: Showing Squares on each side of a Triangle.  Missing results for the Square on the Hypotenuse.  Exercise: Find the length of the Hypotenuse.

 

3: Showing Squares on each side of a Triangle.  Missing results for the Square on one of the Shorter sides. Exercise: Find the length of the Shorter side.

 

 

Section 8

 

1. Six ideas about Parallelograms

Coordinate Geometry

 

1. Coordinating the Plane – Placing the Origin – Drawing Axes

 

2. Plot points on the x-axis

 

3. Plot points on the y-axis

 

4. Plotting points

Filling in Formulae

 

1. See how to fill in numbers in the Distance Formula

 

2. Input your own numbers and Fill in the Distance Formula

 Examining a Line Equation

 

1. See the values of Slope and Constant vary

 

2. See how Slopes and Constants of Parallel lines are Connected

 

3. See how slopes of Perpendicular Lines are Connected

 

4. See the Points of Intersection with the Axes

 

5. Find the point of intersection of Two Lines

Geometry Extra

 

1.      Pythagorean Triples and Incircles (direct link to file; concept supplied by John Courlander)

 

2.     Examining a Protractor

 

Functions and Graphs

1. Function Calculator –Input/Output/Graph

 

2. Horizontal Line f(x) = Constant

 

3. Vertical Line x = Constant

(This is not a function)

 

4. Linear Functions: y = mx + c

 

5. Quadratic Functions: y=ax2+bx+c

 

6. Cubic Functions: y=ax3+bx2+cx+d

 

7. Best Placing of Ball for Rugby Conversion Kick.

 

8. Blank Grid

Trigonometry

 

 

1. Showing Trigonometric Ratios as Lengths of Segments

 

2. Showing Trigonometric Ratios as Lengths of Segments: File 2

 

 

3. Showing the Sine Wave connected to the Sine Length

 

4. Showing the Cosine Wave connected to the Cosine Length

 

5. Showing the Tangent Wave connected to the Tangent Length

 

6. Showing Slope as Tangent Lengths

 

7. Investigating the Unit Circle

 

8. Estimating Angles

Differentiation

 

1. Derivative of a Quadratic Function

 

2.. Tangent slope as limit of Secant slope

 

3. Examining a Cubic Curve with derivatives

 

4.. The Differentiation Process

 

5.1  Showing Derivatives of a Cubic Function File 1: The Slope of the Cubic Function

 

5.2  Showing Derivatives of a Cubic Function File 2: The Cubic and its Derivative, the Quadratic Function

 

5.3  Showing Derivatives of a Cubic Function File 3: The Slope of the Quadratic Function

 

5.4  Showing Derivatives of a Cubic Function File 4: The Second Derivative of the Cubic – the Linear Function

 

5.5  Showing Derivatives of a Cubic Function : Showing First and Second Derivatives; Changing the Cubic Function

 

5.6 The Experience of Differentiation

Algebra

 

1.1 The Principle of a Balance or See-saw

 

1.2 Making Changes to a Balanced See-saw: Solving an Equation: Type 1 – Equal Changes on Both Sides

 

1.3  An Unusual Balance with Nothing on One Side

 

1.4 Making Changes to a Balanced See-saw: Type 2 – Reversing Operations on Transfer of Sides

 

1.5 Making Changes to a Balanced See-saw: Solving an Equation: Type 2 – Reversing Operations on Transfer of Sides

 

2.1 Pre-algebra for Simultaneous Equations

 

2.2 Simultaneous Equations

Graph Drawing

 

1. See how Percentage Changes in Speed affect the Time taken for a Journey

 

2. Properties of a Quadratic Graph – Part 1

 

3. Properties of a Quadratic Curve – Part 2

 

Measure

 Examining π

 

1. Unfold a Circle to see the connection of Radius and Diameter with π

 

2. See the area of an unfolded circle as the area of a Triangle

Income Tax

1.2 Slide Blocks to see Tax Calculation

Writing Text

Static Text

Dynamic Text

LaTeX

 

 

 

Page created by Neil Hallinan © 2010