Difference between revisions of "GeoGebra-5.04/C2/Properties-of-Quadrilaterals/English"

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Point to the segment AB.  
 
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* To construct quadrilaterals  
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'''Spoken Tutorial workshops'''  
 
'''Spoken Tutorial workshops'''  
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||The '''Spoken Tutorial Project '''team conducts workshops using spoken tutorials and gives certificates.  
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* gives certificates.  
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For more details, please write to us.  
 
For more details, please write to us.  

Revision as of 08:02, 12 July 2018

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this tutorial on Properties of Quadrilaterals in GeoGebra.
Slide Number 2

Learning Objectives

In this tutorial we will learn,
  • To construct quadrilaterals and
  • understand the properties of quadrilaterals using GeoGebra.
Slide Number 3

System Requirement

Here I am using:
  • Ubuntu Linux OS, version 14.04
  • GeoGebra version 5.0.438.0-d
Slide Number 4

Pre requisites

www.spoken-tutorial.org.

To follow this tutorial, learner should be familiar with GeoGebra interface.


If not for relevant GeoGebra tutorials, please visit our website.

Let us begin our demonstration.
Cursor on the Graphics view. I have already opened the GeoGebra interface.


For this tutorial, I will first uncheck the Axes.

Right-click on Graphics view.

Graphics menu opens.

Click on Axes check-box.

To do that, right-click on Graphics view.

The Graphics menu opens.

Click on the Axes check-box.

Cursor on GeoGebra interface. I will increase the font size for better view.
Click on the options menu >> click on font size >> on 18 pt radio button. Go to Options menu, navigate to Font Size.

From the sub-menu, select 18 pt radio button.

Cursor on GeoGebra interface. Now let us construct a parallelogram.
Click on Segment with Given Length tool.

Click on Graphics view.

Click on the Segment with Given Length tool.

Click on the Graphics view.

Point to the text box.


Type 5 in Length field >> click OK.

Point to segment f.

The Segment with Given Length text box opens.


In the Length field, type 5 and click on OK button.


Segment AB with length 5 cm and labelled as f, is drawn.

Point to the point on the Graphics view. Let us delete the point that was drawn mistakenly.

This point may not be required for the actual drawing.

Right-click on the point.

From sub-menu >> select Delete option.

Right-click on the point.

From the sub-menu, select the Delete option.

click on Parallel line tool>> click on AB >> point C.

Click on line AB.

Next click on the Parallel Line tool.

Click below line AB to draw point C then click on line AB.

Point to the parallel line. A parallel line to segment AB passing through C, is drawn.
Click on Segment tool >> click on A >> Click on C. Using Segment tool, join the points A and C.
click on Parallel Line tool >> click on segment AC >> point B. Click again on Parallel Line tool, click on segment AC and then click on point B.
Point to the Parallel line and intersection point. Two parallel lines g and i intersect at a point.
Click on Intersect tool>> click on the point of intersection as D. Click on Intersect tool and click on the point of intersection as D.
Click on Segment tool >> click points C and D >> D and B. Now using the Segment tool, join the points, C, D and D, B.
Point to the Parallelogram. Parallelogram ABDC is now complete.
Cursor on Graphics view We will hide the lines g and i, so that we can see the parallelogram clearly.
Right-click on line g and click on Show Object check-box.


Right-click on line i >> click on Show Object check-box.

Right-click on line g, from the submenu click on Show Object check-box.


Similarly I will hide the line i.

Point to the parallelogram ABDC. Now we will explore the properties of parallelogram ABDC.
Point to the line segments f, j, h, k in Algebra view.

Point to lines in Graphics view.

From the Algebra view, we can find that,
  • segments f and j are equal and
  • segments h and k are also equal.

Observe that, the opposite sides are parallel and equal.

Cursor on the parallelogram. Let us now measure the angles of the parallelogram.
Click on Angle tool.

Click on ACD, CAB, ABD, BDC.

Click on Angle tool.

Click on the points DCA, CAB, ABD, BDC.

Point to the sides and angle in the parallelogram. Observe that the opposite angles are equal.
Cursor on the parallelogram. Now we will convert the parallelogram ABDC to a rectangle.
Click on Move tool >> click and drag point C.

Click and drag labels.

Point to all the angles of the rectangle ABDC.

Click on Move tool.

Click and drag point C until you see 90 degrees angle.


Drag the labels to see them clearly.


Observe that all the angles changed to 90 degrees.

Cursor on GeoGebra interface. Now let us learn to construct a kite.
Click on File >> Select New Window. For this I will open a new GeoGebra window.

Click on File and select New Window.

Cursor on Graphics view. To contruct a kite, we will draw two circles that intersect at two points.
Click on Circle with Centre through point tool. Click on Circle with Centre through point tool.
Click on the Graphics view. Then click on Graphics view.
Cursor on point A Point A is drawn, this is the centre of the circle.
Click again at a distance. Click again at some distance from point A.
Cursor on point B. Point B appears.

This completes the circle c.

Click on Circle with Centre through point tool >> Graphics view.

Cursor on point C >> Click again at a distance >> Cursor on point D.

Similarly, we will draw another circle with centre C and passing through point D.
Point to the two points of intersection Notice that the two circles c and d intersect at two points.
Click on Intersect tool and click on the circles c and d. Click on Intersect tool and click on the circles c and d.
Cursor on the points of intersection. E and F are the intersection points of the circles.
Point to the circles. Now let us draw the required quadrilateral using these circles.
Click on Polygon tool. Click on Polygon tool.
Click on the points A, E, C, F and A again. Click on the points A, E, C, F and A again to complete the quadrilateral.
Point to the Algebra view. Notice in the Algebra View that two pairs of adjacent sides are equal.


The drawn quadrilateral is a kite.

Slide Number 5

Assignment

Pause the tutorial and do this assignment.

1. Measure the angles of the kite and check what happens.

2. Draw diagonals and locate the intersection point of the diagonals.

3. Measure the angle at the intersection of the diagonals.

4. Check if diagonals bisect each other.

Show the completed assignment. Your completed assignment should look like this.
press Ctrl + A >> Delete key. To delete all the objects, press Ctrl + A and then press Delete key on the Key board.
Cursor on Graphics view. Now let us construct a rhombus.
Click on Segment with Given Length tool.

Click on Graphics view.

Click on Segment with Given Length tool.

Click on the Graphics view.

Point to the text box. Segment with Given Length text box opens.
Type Length as 4 >> click OK.

Point to the segment AB.

In the Length field, type 4 and click on OK button.

A segment with 4 units is drawn.

Cursor on Graphics view. Let us construct a circle with center A and passing through point B.
Click on Circle with Centre through Point tool.

Click on point A and B.

Point to the circle c.

Click on Circle with Centre through Point tool.


Click on points A and B to complete the circle.

Click on Point tool >> click on circumference of circle. Using Point tool, mark a point C on the circumference of the circle.
Click on Segment tool >> click on A >>click on C. Click on Segment tool and then click on points A and C.

This will join the points A and C.

Select Parallel Line tool from

toolbar >> click on point C >> segment AB.

Click on the Parallel line tool and click on the line AB and then on point C.

We see a line parallel to AB passing through C.

Select Parallel Line tool from toolbar.

Click on point B >> segment AC.

Similarly, draw a parallel line to segment AC passing through point B.
Point to the point of intersection.

Click on Intersect tool >> click on point of intersection.

Notice that the lines i and h intersect at a point.

Using Intersect tool, we will mark the point of intersection as D.

Click on Segment tool>> join points.

A, D and B, C.

Using the Segment tool, join the points A, D and B, C.
Point to the quadrilateral and its diagonals. A quadrilateral ABDC with diagonals AD and BC is drawn.
Point to the intersection point.

Click on Intersect tool >> click on intersection point.

The diagonals intersect at a point.


Using Intersect tool, mark the point of intersection as E.

Slide Number 6

Assignment

Pause the tutorial and do this assignment.


1. Check if the diagonals of the quadrilateral ABDC bisect each other.

2. Also check if the diagonals are perpendicular bisectors.

Show the completed assignment. Your completed assignment should look like this.
Cursor on Graphics view. Now let us construct a cyclic quadrilateral.
For this, let us open Graphics 2 view.
Click on View menu >> click on check-box Graphics 2. Go to View menu and select Graphics 2 check box.


Graphics 2 view window opens, next to existing Graphics view.

Drag border of the existing Graphics view. Drag the border of the existing Graphics view, to see Graphics 2 view.
Select Regular Polygon tool >> click on any two points on Graphics view. Now select Regular Polygon tool.


Click twice on Graphics 2 view.

Point to the text box and value.


Click on OK.

The Regular Polygon text box opens with default value 4.


Click on the OK button.

Point to the square. A square FGHI is drawn in Graphics 2 view.
Point to FG and GH. Let's construct perpendicular bisectors to segments FG and GH.
Select Perpendicular bisector tool from the tool bar.


Click on the point F, G >> click G, H.

Select the Perpendicular Bisector tool from the tool bar.


Click on the points F, Gand G, H.

Point to the intersection point. Observe that the perpendicular bisectors intersect at a point.
Click on Intersect tool >> click on point of intersection of bisectors. Using Intersect tool we will mark this point as J.
Point to J and F. Let's now construct a circle with centre as J and passing through F.
Click on Circle with center through Point tool >> click on point J >> click on point F. Click on the Circle with center through Point tool, click on point J.


Then click on point F.

Point to the cyclic quadrilateral FGHI. A cyclic quadrilateral FGHI is drawn.
Cursor on the quadrilateral FGHI. Now we will display its area.
Click on Area tool from the Angle tool drop down.


Click on the quadrilateral FGHI.

Point to the area value.

Click on the Area tool from the Angle tool drop down.

Then click on the quadrilateral FGHI to display its area.

Slide Number 7

Assignment

As an assignment,
  • Draw a trapezium
  • Measure its perimeter and area.
Show the completed assignment. Your completed assignment should look like this.
Let us summarise what we have learnt.
Slide Number 8

Summary

In this tutorial we have learnt,
  • To construct quadrilaterals
  • and understand the properties of quadrilaterals using GeoGebra.
Slide Number 9

About Spoken Tutorial project

The video at the following link summarises the Spoken Tutorial project.

Please download and watch it.

Slide Number 10

Spoken Tutorial workshops

The Spoken Tutorial Project team conducts workshops using spoken tutorials and gives certificates.

For more details, please write to us.

Slide Number 11

Forum for specific questions:

Do you have questions in THIS Spoken Tutorial?

  • Please visit this site
  • Choose the minute and second where you have the question
  • Explain your question briefly
  • Someone from our team will answer them
Please post your questions in this forum.
Slide Number 12

Acknowledgement

Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.

Contributors and Content Editors

Madhurig, Nancyvarkey

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