GeoGebra course (EN)
[b][color=#b20ea8]GeoGebra course, introduction to geometry. Press the different sections in order to carry out the activities.[/color][/b] Translated by Chelo Talavera Peñaranda
Table of Contents
- A. First steps with GeoGebra
- A1. The "Move" tool
- A2. The "Delete" tool
- A3. The "Point" tool
- A4. The "Segment" tool
- A5. The “Distance or Lenght” tool
- A6. The "Ray" tool
- A7. The "Line" tool
- A8. The "Perpendicular Line" tool
- A9. The "Parallel Line" tool
- A10. The "Animation on" option
- A11. The "Perpendicular Bisector" tool
- A12. The "Midpoint or centre" tool
- A13. The "Intersect" tool
- A14. The "Polyline" tool
- A15. The "Angle" tool. The acute angle
- A16. The “Angle” tool. The right angle
- 17. The “Angle” tool. The obtuse angle
- A18. The “Angle” tool. The straight angle
- A19. The "Bisector" tool (1)
- A20. The "Bisector" tool (2)
- B. The polygons
- B1. The "Polygon" tool
- B2. The "Area" tool
- B3. The "Regular Polygon" tool
- B4. The "Centroid" command
- B5. The apothem of a regular polygon
- B6. The barycentre
- B7. The orthocentre
- B8. The Varignon theorem
- C. The Cercle
- C1. The "Circle with Centre through Point" tool
- C2. The "Circle with Centre and Radius" tool
- C3. “Compass” tool
- C4. The "Circle through 3 points" tool
- C5. The "Semicircle through 2 points" tool
- C6. The "Circumcircular Arc" tool
- D. Symmetries
- D1. La herramienta "Vector"
- D2. The “Slider” tool
- D3. The "Transtale by Vector" tool
- D4. The "Reflect Object in Line" tool
- D5. The slider reflection
- D6. The "Rotate around Point" tool
- D7. The inversion around a point. The "Reflect Object in Point" tool
- D8. The identity symmetry
- D9. The translational symmetry
- D10. The reflectional symmetry
- D11. The rotational symmetry
- D12. The sliding reflectional symmetry
A1. The "Move" tool
[size=200][b]Move the point[/b][/size][br][br][color=#000000][b]Welcome to GeoGebra[/b]. GeoGebra is more than a dynamic geometry computing application. GeoGebra has more than one hundred commands (instructions you can write), but only a few commands have its own tool (Small square button located at the top of the graphic window). You will begin to study the use of the tools. Look at the Graphics View ([color=#008000][b]green[/b][/color]) and above the "Move" tool [icon]/images/ggb/toolbar/mode_move.png[/icon], surrounded by a blue square indicating that it is activated.[/color][br][br][color=#000000]In the Graphics View you can see a circumference and an outer point. Just follow the numbered instructions.[/color][br][br][color=#9900ff]1st. Move the point to the inner part of the circumference.[/color][br][br][color=#000000]The two curved arrows located in the upper right corner of the Graphics View allow you to reset the activity.[/color][br][color=#000000]If the activity is correct, you will get 10 points automatically.[/color]
B1. The "Polygon" tool
[size=200][b]Draw a triangle called "T"[/b][/size][br][br][color=#000000]With GeoGebra you can draw polygons by clicking the position of the vertices, but to inform GeoGebra that you have finished the polygon, you must click on the first point.[/color][br][br][color=#9900ff]1st. Activate the "Polygon" tool.[icon]/images/ggb/toolbar/mode_polygon.png[/icon].[/color][br][br][color=#9900ff]2nd. Click on three non-aligned points in the Graphics View and then click again on the first point. The points "A", "B", "C", the segments "a", "b", "c" and the polygon will appear.[/color][br][br][color=#9900ff]3rd Activate the "Move" tool [icon]/images/ggb/toolbar/mode_move.png[/icon]. Right-click inside the triangle to open the Context Menu and name it "T".[/color][br][br][color=#000000]The two curved arrows located in the upper right corner of the Graphics View allow you to reset the activity.[/color][br][color=#000000]If the activity is correct, you will get 10 points automatically.[/color]
C1. The "Circle with Centre through Point" tool
[size=200][b]Draw a circle centred on point "A" that passes through point "B"[/b][/size][br][br][color=#000000]You only need two clicks to draw it. In this activity you will learn to create dynamic texts. A text is an expression closed between double quotes, and has a very interesting property, you can add numbers in the texts.[/color][br][br][color=#9900ff]1st. Activate the "Circle with Centre through Point" tool [icon]/images/ggb/toolbar/mode_circle2.png[/icon].[/color][br][br][color=#9900ff]2nd. Click on two different points in the Graphics View. You will see the centre "A", the point "B" through which it runs and the circle called "c".[/color][br][br][color=#9900ff]3rd. Activate the "Move" tool [icon]/images/ggb/toolbar/mode_move.png[/icon] and type into the Input Bar the command [color=#000000][b]t1=FormulaText("Perimeter =" + Perimeter(c) + "cm")[/b][/color] in order to know the perimeter of the circumference.[/color][br][br][br][br][color=#000000]Texts also have a name in GeoGebra, this is called [color=#000000][b]t1[/b][/color]. The first term, [color=#000000][b]"Perimeter ="[/b][/color], closed into quotation marks, is a static text that indicates the name of the property you want to write. The second term, [color=#000000][b]Perimeter(c)[/b][/color], is dynamic and calculates the property. The third term, [color=#000000][b]"cm"[/b][/color], is also a static text that indicates the unit of measurement.[/color][br][br][color=#000000]Activate the "Move" tool [icon]/images/ggb/toolbar/mode_move.png[/icon] and move the points, you will check how the perimeter of the circle is constantly updated.[/color][br][br][color=#000000]The two curved arrows located in the upper right corner of the Graphics View allow you to reset the activity.[/color][br][br][color=#000000]If the activity is correct, you will get 10 points automatically.[/color]
D1. La herramienta "Vector"
[size=200][b]Dibuja un vector[/b][/size][br][br][color=#000000]Un vector es un segmento orientado, tiene dirección como los segmentos (inclinación del segmento) y un sentido marcado por una punta de flecha (orientación).[/color][br][br][color=#9900ff]1º. Activa la herramienta "Vector" [icon]/images/ggb/toolbar/mode_vector.png[/icon], situada en la familia de la recta.[/color][br][br][color=#9900ff]2º. Pulsa la ventana gráfica para situar el punto de origen del vector. Será el punto "A".[/color][br][br][color=#9900ff]3º. Pulsa otra posición para situar el sentido del vector. Será el punto "B", observarás una flecha que se llama "u" desde el punto "A" hasta al punto "B".[/color][br][br][color=#000000]Las dos flechas semicirculares situadas en la parte superior derecha de la ventana gráfica permiten restablecer la actividad.[/color][br][color=#000000]Si la actividad está correcta tendrás 10 puntos de forma automática.[/color]