# GeoGebra 5.04

GeoGebra

GeoGebra brings together Geometry, Algebra, Calculus, spreadsheets, graphing, statistics and probability applications in a single package. GeoGebra provides different views for various mathematical objects.

Teachers and students can use GeoGebra to make conjectures and to understand how to prove geometric theorems. A object in GeoGebra is displayed in different representations (e.g. algebraic and graphical). These representations are linked dynamically. Equations and coordinates can be entered and modified directly on screen or through the Input bar. GeoGebra Classic’s user interface provides a variety of dialog boxes. It has different accessibility features. The keyboard shortcuts allow us to access many features of GeoGebra conveniently.

GeoGebra is available for download at www.geogebra.org.

Contributors, Content Editors and Reviewers

The Spoken Tutorial effort for GeoGebra 5.04 is being contributed by Ms. Madhuri Ganapathi, Ms. Nancy Varkey, Dr. Vidya Iyer and Mr. Kaushik Datta from IIT Bombay.

## Contents

## Basic Level

**1. Introduction to GeoGebra**

- About GeoGebra interface

- Menu bar and Geometric tools

- Open GeoGebra interface in Ubuntu Linux and windows 10 OS

- How to delete objects

- Enable and disable grid and axes

- Algebra and Graphics views

- Change object properties of lines

- Draw parallel and perpendicular lines

- Dependent and independent objects

- Properties of Graphics view

**2. Basics of Triangles **

- Increase the font size using the Options menu

- Draw a triangle

- Measure the angles of the triangle

- Display area and perimeter on the triangle

- Show that sum of the interior angles is 180 degrees

- Show that exterior angle is equal to sum of interior opposite angles

- Draw external lines to the sides of the triangle

- Draw altitudes to the triangle

- Locate the orthocenter of the triangle

- Draw angle bisectors to the angles of the triangle

- Draw an incircle to the triangle

**3. Congruency of Triangles **

- Define congruency of triangles

- Construct and prove Side Side Side rule of congruency

- Construct and prove Angle Side Angle rule of congruency

- construct and prove Side Angle Side rule of congruency

**4. Properties of Quadrilaterals **

- Construct a parallelogram using parallel lines

- Convert a parallelogram to a rectangle

- Delete mistakenly drawn points

- Construct a kite using intersecting circles

- Explain the properties of a kite

- Construct a rhombus with a given length

- Show properties of a rhombus

- Explain how to open and use Graphics 2 view

- Construct a cyclic quadrilateral and display its area

**5. Types of Symmetry **

- Definition of symmetry

- Definition of line of symmetry

- Reflect an object about a line

- Change properties of an object

- Reflect an object about a point

- Reflect an object a circle

- Definition of rotation symmetry

- How to create a slider

- Rotate an object around a point

- Translation of an object by a vector

- Definition of scale symmetry

- Dilate an object by a factor

** 6. Polynomials **

- Define a polynomial

- Find the slope of a linear polynomial

- Define the degree of a polynomial

- Use of input bar to type and display polynomials

- Find the degree of a polynomial

- Find the zeros of a polynomial

- Find the roots of a polynomial

- Use Remainder theorem to divide polynomials

- Factorization of polynomial

** 7. Theorems in GeoGebra **

- State Pythagoras theorem

- Prove Pythagoras theorem

- State Midpoint theorem

- Prove Midpoint theorem

- Show Construction Protocol for the drawn figure