How to: Geometry tools

GeoGebra Institute of MEI, Mar 8, 2016

Table of Contents

  1. Introduction
    1. Introduction
  2. Examples
    1. Tangent and radius are perpendicular
    2. Enlargement scale factor a from (0,0)
    3. Dissection proof of Pythagoras
    4. Parabolic car headlamp
  3. Skills
    1. Geometry tools
  4. Constructions
    1. Construction task 1: Angle in a semi-circle
    2. Construction task 2: Reflection in y = x
  5. Tasks
    1. Tasks
    2. Construction problem

1.

Introduction

  • 1. Introduction

1.1.

Introduction

In this lesson you will be introduced to the using the geometry tools in GeoGebra and practise using the Graphics Styling bar.[br][br]Some examples of GeoGebra files are displayed in section 2 to give you a sense of what can be achieved.  You should then work through the skills and constructions section before trying the tasks.
– GeoGebra Institute of MEI

2.

Examples

  • 1. Tangent and radius are perpendicular
  • 2. Enlargement scale factor a from (0,0)
  • 3. Dissection proof of Pythagoras
  • 4. Parabolic car headlamp

2.1.

Tangent and radius are perpendicular

– GeoGebra Institute of MEI

2.2.

–

2.3.

–

2.4.

–

3.

Skills

  • 1. Geometry tools

3.1.

Geometry tools

Using the Geometry tools
The Graphics view features tools (the square buttons at the top).  These can be used to add geometrical objects to the Graphics view.  To change the tool click on a different button.  Related tools are contained in each button.[br][br]Experiment with this by adding some different geometrical objects to the screen.
– GeoGebra Institute of MEI

4.

Constructions

  • 1. Construction task 1: Angle in a semi-circle
  • 2. Construction task 2: Reflection in y = x

4.1.

Construction task 1: Angle in a semi-circle

Construction steps
[list=1][*]Use Semi-Circle Through 2 Points (6th menu) to add a semi-circle to the screen end-points A and B.[br][br][/*][*]Use Point (2nd menu) to add a new point on the circle, C.[br][br][/*][*]Use Segment (3rd menu) to create segments AB, AC and BC.[br][br][/*][*]Use the Angle tool (8th menu) to measure the angle ACB.[br][/*][/list]
– GeoGebra Institute of MEI

4.2.

–

5.

Tasks

  • 1. Tasks
  • 2. Construction problem

5.1.

Tasks

Create dynamic files that demonstrate:[br][br][list=1][*]Some of the circle theorems.[br][br][/*][*]Different transformations of shapes in a plane.[br][br][/*][*]Similar triangles.[br][br][/*][*]Properties of quadrilaterals.[/*][/list]
– GeoGebra Institute of MEI

5.2.

–

Information