# GB GeoGebra Tutorials

Mathematics and Multimedia GeoGebra Step-by-Step Tutorial Series
The objective of the GeoGebra Step-by-Step Tutorial Series is not only to teach the readers how to use the software, but also to suggest how to use GeoGebra in teaching and learning mathematics. Most of the tutorials are (or will be) linked to related articles containing explanations and proofs about the mathematics discussed in the tutorials.
Although, it is advisable to follow the tutorial series chronologically, the reader may opt for any tutorial of choice since each tutorial is designed to be independent from each other. The readers may start from any tutorial, and follow it step-by-step even without learning the tutorials prior to it.
Unlike other blogs, all the tutorials in Mathematics and Multimedia, as well as all the articles, are constantly updated and modified for further improvement. This series is not yet complete, its arrangement maybe changed from time to time, but rest assured that more tutorials will be posted.
What's New

A. FOR BEGINNERS
I. GeoGebra Essentials Tutorial Series
 Introduction to GeoGebraThis is the introduction to GeoGra. It contains discussions of the different parts of GeoGebra and the advantages in using it. It also points you out to the system installation requirements and the website where you can download it. GeoGebra Essentials 1 – Locating the Triangle’s CentroidThis tutorial, we are going to create a triangle and find its centroid or the intersection of its medians. In doing the tutorial, we are going to learn how to use the following tools: use the new point tool, segment between two points tool, midpoint tool, intersect tool and move tool. GeoGebra Essentials 2 – Constructing a RectangleIn this tutorial, we are going to create a rectangle using the segment tools, the parallel and perpendicular line tools. We are going to learn how to measure the length of segments and angles. In doing the tutorial, we are also going to discuss semi-free objects. GeoGebra Essentials 3 – Triangles, Incircles and CircumCirclesIn this tutorial, we are going to show that in any triangle, we can always create a circle passing through its three vertices, and we can always create a circle inscribed in it. The circle that passes through the three vertices of a triangle is called the circumcircle of the triangle, while the circle that inscribed in it is called its incircle. GeoGebra Essentials 4 –Angles, Lengths and Object PropertiesIn this tutorial, we will use GeoGebra to investigate if a relationship exists between the interior angles of a triangle and the lengths of its sides. We are going to learn two new tools – the Angle and the Distance or Lengthtool. GeoGEbra Essentials 5 – The Compass Tool and the SSS CongruenceIn this tutorial, we will mimic compass and straightedge construction using GeoGebra’s compass, and segment between two points and ray through two points tool. We will use the concept of the SSS congruence; that is, we will show that if the three corresponding sides of a triangle are congruent, then the triangles are congruent. GeoGebra Essentials 6 –Sliders and RhombusesIn this tutorial, we will construct a rhombus using two sliders – the angle slider and the number slider. The slider the slider tool. A slider (see figure below) is a dynamic graphical representation of a number. GeoGebra Essentials 7– Using the Keyboard CommandsIn this post, we are going to learn how to construct mathematical objects using keyboard commands. We will learn how to In particular, we are going to create an equilateral triangle. GeoGebra Tutorial 8 – Graphs and their PropertiesIn this tutorial, we are going to learn the basics about graphing and how to use GeoGebra command to get the critical points and the derivative of functions. We will also learn how to graph trigonometric, exponential, and logarithmic functions. GeoGebra Essentials 9 – Texts and VariablesIn this tutorial, we are going to learn how to use the text tool of GeoGebra. We will learn about constants and variables and will learn how to concatenate them in Geogebra codes. GeoGebra Tutorial 10 – Exporting Your Document
II. Basic Geometric Figures Constructions
1. Introduction to Basic Construction: Construction versus Drawing
2. GeoGebra Basic Construction 1 – Constructing an Equilateral Triangle
3. GeoGebra Basic Construction 2 – Constructing an Isosceles Triangle
4. GeoGebra Basic Construction 3 – Constructing a Right Triangle
5. GeoGebra Basic Construction 4 – Constructing a Square
6. GeoGebra Basic Construction 5 – Constructing a Rectangle
7. GeoGebra Basic Construction 6 - Constructing a Parallelogram
8. GeoGebra Basic Construction 7 – Constructing a Rhombus
9. GeoGebra Basic Construction 8 – Constructing a Trapezoid
10. GeoGebra Basic Construction 9 – Constructing a Kite
B. FOR BEGINNERS/INTERMEDIATE USERS
I. GeoGebra Intermediate Tutorial Series
GeoGebraTutorial 1Midpoints and Quadrilaterals In this tutorial, we will use GeoGebra to investigate the properties of the polygon formed by connecting consecutive midpoints of sides of a quadrilateral. The tools that we will use in this construction are new point, segment between two points, midpoint or center, and polygon, distance tool and angle tool.

GeoGebra Tutorial 2 – Constructing an Equilateral Triangle In this tutorial, we will mimic compass and straightedge construction by using radii of two congruent circles to construct an equilateral triangle. The tools that we will use in this tutorial are new point,polygon, circle with center through point.
GeoGebraTutorial 3 – Constructing a Square This construction is similar to Tutorial 2, mimicking the compass and straightedge construction. In this construction, we will use a circle and perpendicular and parallel lines to construct a square. The tools that we will use in this tutorial arenew point, circle with center through point,segment between two points,perpendicular line and parallel line.

GeoGebra Tutorial 4 – Graphs and Sliders In this tutorial, we learn how to use the input box to graph linear functions. We will use the sliders to show the effects of the values of m and b to the graph of the function y = m x + b. In this tutorial, you will learn the advantages of GeoGebra over others. The tool use in this tutorial is the slider.

GeoGebraTutorial 5 – Discovering the Pythorean Theorem In this tutorial, we will investigate the relationship among the area of the squares formed by the three sides of a right triangle. The tool that we will use in this tutorial are perpendicular line,segment between two points, and regular polygon.

GeoGebra Tutorial 6 – Parameterization of Area and Length of a Rectangle In this tutorial, we will learn how to write equations, formulas and perform computations in GeoGebra. We will construct a rectangle with a fixed perimeter and a variable length. We will graph the ordered pair (length,area) of a rectangle with a fixed perimeter in the xy-plane and find the dimensions with the maximum area. The tools that we will use in this tutorial are new point,perpendicular line, parallel line, andpolygon.

GeoGebra Tutorial 7 – Sliders, Rotation and the Angle Sum Theorem In this tutorial, we will use the slider tool and rotation to replicate triangles, rotate them and show that the angle sum of a triangle is 180 degrees. The tools that we will use in this tutorial are line through two points, midpoint or center,polygon, slider, and rotate object around a point by angle.

GeoGebra Tutorial 8 – Tracing Graphs of Trigonometric Functions In this tutorial, we will trace paths of points formed by coordinates of the distance d traveled by a point along the circumference of a circle. We will graph (d,x) and (d,y) where x and y are the xand y-coordinates of the points . The tools that we will use in this construction are new point, circle with center through point, and circular arc with center through two points.
GeoGebra Tutorial 9– Vector and TranslationIn this tutorial, we will use the vector tool to translate a triangle. We will explore the relationship among the coordinates of the pre-image of an object, the object of its image, and the direction and magnitude of the vector. The tools that we will use in this tutorial are new point, polygon, vector between two points, translate object by vector.

GeoGebraTutorial 10 – Vectors and Tessellation In this tutorial, we will use the strategy that we have learned in the Vector and Translation tutorial to tile a plane with regular octagons and squares. The tools that we will use in this tutorial are newpoint, polygon, vector between two points,translate object by vector and regular polygon.

GeoGebra Tutorial 11 – Sliders and Graphs of Trigonometric FunctionsIn this tutorial, we will use the slider to investigate the effects of the parametersa, b, c and d in the graph of the sine function f(x) = a sin(bx -c) + d. We will also explore the cosine and tangent functions of the same form. We will learn how to use check boxes to show and hide the graphs. The tools that we will use in this tutorial are slider and check box to show/hide objects.

GeoGebra Tutorial 12 – Pictures and Angle Measures In this tutorial, we will learn how to insert text and picture in GeoGebra. We will use the protractor image to measure the angle formed by two segments. The tools that we will use in this tutorial are line through two points, segment between two points, angle, and semicircle through two points.

GeoGebra Tutorial 13– How to Use Latex in GeoGebraIn this tutorial, we will learn how to embed Latex in GeoGebra worksheets. Latex is a typesetting program capable of constructing complicated mathematical formulas. It is widely used by mathematicians in creating scientific documents. It can also be embedded in websites and is integrated in many mathematics programs.

GeoGebra Tutorial 14 – Circle Area Approximation by Inscribed Polygons
In this tutorial, we are going to inscribe a polygon in a circle, increase its number of sides, and see the relationship between the area of the circle and the area of the polygon as the number of sides increases. This strategy was done by mathematicians in ancient time to approximate the area of a circle.

GeoGebra Tutorial 15 – Tangents, Circles and Circumscribed Polygons
This tutorial is a continuation of GeoGebra Tutorial 14. In this tutorial, we are going to compare the areas of the circle, its inscribed polygon which we constructed in Tutorial 14 and its circumscribed polygon.

GeoGebra Tutorial 16 – Slider, Sequence and Segment DivisionIn this tutorial, we are going to learn how to use the slider control and the sequence command to divide a segment with an arbitrary length into n equal partitions.

GeoGebra Tutorial 17 -Tangent and the Meaning of Derivative
In this tutorial, we are going to construct point A on a function, and construct a line tangent to the function and passing through A. We are also going to plot a point whose x-coordinate is is the x-coordinate of point A and the y-coordinate is the slope of the tangent line. We are going to get the derivative of the function and relate it to the path of the second point.

GeoGebra Tutorial 18 – Area Under a Curve and the Riemann SumsIn this tutorial, we are going to compare the area of a plane under a curve f(x) = x2 bounded by the x-axis and the line x =1 with the sum of the areas of rectangular partitions under the same boundaries.

GeoGebra Tutorial 19 – Introduction to SpreadsheetIn this tutorial, we are going to use the Record to Spreadsheet tool to record the coordinates of a moving point along the graph of a particular function. We will graph the function f(x) = x2, construct point P with coordinates(a,f(a)) , where a is a value from a slider. We will record the coordinates of the traces of P .

GeoGebra Tutorial 20 –Spreadsheet, Slider and Curves of Best FitIn this tutorial, we will use the spreadsheet window to input coordinates of points that will be plotted in the coordinate plane. We will use the Best Fit Line tool to construct a line of best fit of the plotted points. Finally, we will also use the Fitpoly command and the slider tool to construct polynomial (with varying degrees) curves of best fit.

GeoGebra Tutorial 21 – Spreadsheet and SimilarityIn this tutorial, we will construct a constant number k, in the form of a slider, and see what happens if we multiply the coordinates (x1,y1), (x2,y2) and (x3,y3) of the vertices of our triangle by k. We will investigate if there is a relationship between the original triangle and the triangle formed whose vertices have coordinates (kx1,ky1), (kx2,ky2) and (kx3,ky3).
GeoGebra Tutorial 22 – Spreadsheet, Vectors, and MatricesIn this tutorial, we are going to explore the relationship between the product of two 2 x 2 matrices. We will set the entries of the factor matrices to integers, and limit the second matrix entries to values of -1, 0, and 1. We will also observe the relationship between their graphical interpretations, known as vectors.

GeoGebra Tutorial 23– Spreadsheet, Bar Chart and HistogramIn this tutorial, we are going to use the spreadsheet to perform basic data representation. We will plot a frequency table of grouped data and perform basic computations using the spreadsheet window. After the data is completed, we will construct a histogram.

GeoGebra Tutorial 24– Box and Whiskers

GeoGebra Tutorial 25– The Rolling CircleIn this tutorial, we are going to use GeoGebra in constructing a rolling circle. This way, we would be able to relate the diameter of the circle to its circumference. Moreover, this activity will reinforce the relationship between the angle and radian measure.

GeoGebra Tutorial 26– Constructing a CycloidThis tutorial is very similar to the Tutorial 25. In this tutorial, we are going to use GeoGebra to construct a cycloid.A cycloid is the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line.

GeoGebra Tutorial 27– Animation and EpicycloidsIn this tutorial, we are going to rotate a circle about the center of another circle tangent to it using the animation feature of GeoGebra. Along the rotating circle, we will also rotate a point on its circumference about its center (see red point in the diagram). The path of this point is called the epicycloid.

GeoGebra Tutorial 28– Animation and Hypocycloids

GeoGebra Tutorial 29– Animation, Loci and Radian MeasureIn this tutorial, we are going to introduce the concept of radian. We are going to rotate radius AB’ about point A, the center of the circle. As the point rotates, point C goes back and forth from A to B’at the same speed as that of C. The path of point C traces forms petals.

GeoGebra Tutorial 30 – Loci, Roses and ReflectionsIn this tutorial, we are going to reflect a point on a circle about the x -axis and about the y -axis to form rectangle ABCD. We will construct a segment passing through pointB where one of the endpoints on the center and with length equal to the area of a circle. As we move the point B along the the circle, the trace of the end point of the segment (not on the circle’s center) will form a 4-petal rose.

GeoGebra Tutorial 31 – Paper Folding SimulationIn this tutorial, we are going to use GeoGebra to simulate paper folding. We will represent a rectangular piece of paper with corners ABCD and drag the upper right corner (vertex B) anywhere inside the rectangle. We will use the Point in region tool of GeoGebra 4.0 Beta Release (or New Point tool in 3.2) to construct the figure.

GeoGebra Tutorial 32 – Graphing Piecewise FunctionsIn this tutorial, we are going to use thefunction command of GeoGebra to graph piecewise function
 $f(x) = begin{cases} 1-x, x leq 1 x^2, x > 1 end{cases}$ f(x) = begin{cases} 1-x, x leq 1 x^2, x > 1 end{cases}
.

We will manually create the endpoints and the arrows.