
GeoGebra
Tutorial 1 – Midpoints
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.


GeoGebra Tutorial 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 are new 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.


GeoGebra Tutorial 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 xyplane and find the dimensions with the maximum
area. The tools that we will use in this tutorial are
new point, perpendicular line,
parallel line, and polygon.


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 x and ycoordinates
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 Translation
In this tutorial, we will use the vector tool to
translate a triangle. We will explore the relationship
among the coordinates of the preimage 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.


GeoGebra Tutorial 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 new
point, polygon, vector between two
points, translate object by vector and
regular polygon.


GeoGebra
Tutorial 11 – Sliders and Graphs of Trigonometric
Functions
In this tutorial, we will use the slider to investigate
the effects of the parameters a, 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 GeoGebra
In 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 torial 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
Division
In 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 xcoordinate is is the
xcoordinate of point A and the
ycoordinate 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 Sums
In this tutorial, we are going to compare the area of a
plane under a curve f(x) = x^{2} bounded by the
xaxis and the line x =1 with the sum of the areas of
rectangular partitions under the same boundaries.


GeoGebra Tutorial 19 – Basic Spreadsheet Recording
Spreadsheet programs have the ability to perform
mathematical computations using their cell addresses.
Recently, GeoGebra integrated a spreadsheet in its
graphical user interface, and that is what we are going
to discuss in this tutorial.


Tutorial 20 –
Spreadsheet , Slider and Curves of Best
Fit In 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.


Tutorial 21 – Spreadsheet and
Similarity
In this tutorial, we will construct a constant number
k, in the form of a slider, and see what happens
if we multiply the coordinates
(x_{1},y_{1}),
(x_{2},y_{2}) and
(x_{3},y_{3}) 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
(kx_{1},ky_{1}),
(kx_{2},ky_{2}) and
(kx_{3},ky_{3}).


Tutorial 22
– Spreadsheet, Matrices and
Vectors In 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.


Tutorial 23 –Spreadsheet and
Histogram In 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.


Tutorial 24– Box and
Whiskers


Tutorial 25– The Rolling Circle
In 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.


Tutorial 26– Constructing a Cycloid
This 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.


Tutorial 27 – The Compass Tool and SSS
Congruence


Tutorial 28 – Perpendicular Bisectors and the
Circumcenters


Tutorial 29 – Angle Bisectors and
Incircles


Tutorial 30 – Loci, Roses and Reflections
In 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 4petal rose.


Tutorial 31 – Paper Folding Simulation
In 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.


Tutorial 32 – Perpendicular Bisectors and the
Circumcenters


Tutorial 33 – Angle Bisectors and
Incircles


Tutorial 34 – Treasure Hunt and Circle through
Three Points




