Geogebra/C2/Understanding-Quadrilaterals-Properties/English

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Title of script: Understanding Quadrilateral properties

Author: Madhuri Ganapathi

Keywords: Polygon, Angle, Parallel line, Segment between two points, Insert text, “Distance or Length” tool, New Point, Algebra View, Quadrilaterals, video tutorial

Click here for Slides

Visual Cue Narration
Slide Number 1

Hello everybody.

Welcome to this spoken tutorial on Understanding Quadrilaterals Properties in Geogebra.

Slide Number 2

Note

The intention of this tutorial is not to replace the actual compass box

Construction in GeoGebra is done with the view to understand the properties.

Slide number 3

Pre-requisites

We assume that you have the basic working knowledge of Geogebra.

If not, please visit the spoken tutorial website for relevant tutorials on Geogebra.

Slide number 4

Learning Objectives

In this tutorial, we will learn to construct quadrilaterals
  • Simple quadrilateral
  • Quadrilateral with diagonals
  • Also, learn their properties
Slide Number 5

System Requirement

To record this tutorial I am using

Linux operating system Ubuntu Version 11.10 LTS

Geogebra Version 3.2.47.0

Slide Number 6

GeoGebra Tools used in this tutorial

We will use the following tools of Geogebra for construction

  • Circle with centre through point
  • Polygon
  • Angle
  • Parallel line
  • Segment between two points
  • Insert text
Switch to geogebra window

Dash home >>Media Apps>>

Under Type>>Education>>Geogebra

Let's open a new Geogebra window.

To do this click on Dash home and Media Apps.

Under Type click on Education and then Geogebra.

Click on “Circle with Centre through Point” tool >>

Construct a circle

Let's construct a circle with center 'A' which passes through point 'B'.

To do this, click on the “Circle with Center through Point” tool from toolbar.

Click on the drawing pad. Click on the drawing pad.

Point 'A' is the center.

Click a little away from point A. Then click again and we get point 'B'.

The circle is complete.

Construct circle with center C which passes through D>>

click point C on >>then point D

Let's construct another circle with center 'C' which passes through 'D'.

Click on the drawing pad. It shows point 'C' as the centre.

Click a little away from point C such that

the new circle intersects with the previous circle.

Then click again and we get point 'D'.
Point to the intersection points. The circles intersect at two points.
Click “New Tool” >> select “Intersect Two Objects” Click the “Intersect Two Objects” tool under “New Point”.
Mark the points of intersection. Mark the points of intersection as 'E' and 'F'.
Click on polygon tool Next, click on the “Polygon” tool.
Click on the points A E C F and A again.

Click on the points 'A', 'E', 'C', 'F' and 'A' again.

A simple quadrilateral is drawn.

Point to the “Algebra View” panel. We can see from “Algebra View” that 2 pairs of adjacent sides are equal.

Do you know why? Can you figure out the name of the quadrilateral?

Click on "Save As" >> type "simple_quadrilateral" in file

name >> click on save

Let us save this file now. Click on “File”>> "Save As".

I will type the file name as "simple-quadrilateral" and click on “Save”.

Click on File>>New

Next, let us construct a Quadrilateral with diagonals.

Let's open a new Geogebra window,

by clicking on “File” and ”New ”

Click segment between two points tool>>draw AB Let's draw a segment first.

Select “Segment between Two Points” tool from the toolbar.

On the drawing pad, mark points 'A' and 'B'.

Segment 'AB' is drawn.

Construct a circle with center 'A' >> through point 'B'.

Let's construct a circle with center 'A' which passes through point 'B'.

Click on the “Circle with Centre through Point” tool

To do this click on the “Circle with Centre through Point” tool.

Click on point 'A' and then on 'B'. Click on point 'A' then click on 'B'.
Click on “New Point” tool >> Mark point 'C' on the circumference Using the “New Point” tool,

let's mark a point 'C' on the circumference of the circle.

Click segment between two points>> connect 'AC' Next, using the “Segment between Two Points” tool,
join the points 'A' and 'C'. 
Let's construct a parallel line to segment 'AB' which passes through 'C'.
Click “Parallel Line” tool Select the "Parallel Line" tool from the toolbar.
Click on point C and segment AB. First click on point 'C'

and then click on segment 'AB'.

Click “Parallel Line” tool>>click on point B and segment AC. Let us repeat the process for point 'B'.

Click on point 'B'

and then click on segment 'AC'.

Point to the intersection point >> mark point D Notice that the parallel line to segment 'AB'

and the parallel line to segment AC intersect at a point.

Let's mark the point of intersection as 'D'.
Click “segment between two points” tool >> Connect the points Using the “Segment between Two Points”,

let's connect the points

'A'&'D', 'B'&'C'  

A Quadrilateral ABCD with diagonals AD and BC is drawn.

diagonals intersect at point >>mark the point of intersection Diagonals intersect at a point.

Let us mark the point as 'E'.

Using “Distance or Length” tool,

let's check whether the diagonals bisect each other.

Click on “Angle” tool >> “Distance or Length” tool. Under “Angle”, click on the “Distance or Length” tool.
Click on the points A, E and E, D

Click on the points C, E and E, B

Now, click on the points A, E and E, D

And then click on the points C, E and E, B

Next, we will check whether the diagonals are perpendicular bisectors.
Click “Angle” tool>>measure the angles AEC and CED

To measure the angle, click on the “Angle” tool.

Now, click on the points AEC and then CED

Select the “Move” tool from the toolbar Let's select the “Move” tool from the toolbar.
Use the “Move” tool to move point 'A'. Use the “Move” tool to move point 'A'.
Properties Notice that the diagonals always bisect each other

and are also perpendicular bisectors.

Click on "Save As" >> type "quadrilateral" in filename

>> click on save

Lets save this file now.

Click on “File”>> "Save As".

I will type the filename as "quadrilateral"

click on “Save”.

Slide Number 6

Summary

Lets summarize.

In this tutorial we learnt to construct quadrilaterals using the following tools -

Circle with centre through point, Polygon, Angle,

Parallel line, Segment between two points, Insert text

We also learnt the properties of

*  Simple quadrilateral
*  Quadrilateral with diagonals
Slide number 7

Assignment

To practice- Draw a line segment AB

Mark a point C above the line

Draw a parallel line to AB at C

Mark two points D and E on the Parallel Line

Join points AD and EB , making a trapezium ADEB

Draw perpendicular lines to segment AB from D and E

Mark the points of intersection F and G of the perpendicular lines and AB

Measure distance DE and height DF

Show the output of the Assignment The output should look like this.
Slide number 8

Acknowledgement

Watch the video available at http://spoken-tutorial.org/What is a Spoken Tutorial

It summarises the Spoken Tutorial project

If you do not have good bandwidth, you can download and watch it

The Spoken Tutorial Project Team :

Conducts workshops using spoken tutorials

Gives certificates to those who pass an online test

For more details, please write to

contact@spoken-tutorial.org

Spoken Tutorial Project is a part of the Talk to a Teacher project

It is supported by the National Mission on Education through ICT, MHRD, Government of India

More information on this Mission is available at

http://spoken-tutorial.org/NMEICT-Intro ]

This is Madhuri Ganapathi from IIT Bombay signing off.

Thanks for joining

Contributors and Content Editors

Chandrika, Madhurig