GeoGebra-5.04/C2/Properties-of-Quadrilaterals/English-timed

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Time Narration
00:01 Welcome to this tutorial on Properties of Quadrilaterals in GeoGebra.
00:07 In this tutorial we will learn,

To construct quadrilaterals and understand the properties of quadrilaterals using GeoGebra.

00:19 Here I am using:

Ubuntu Linux OS, version 14.04

GeoGebra version 5.0.438.0-d

00:31 To follow this tutorial, learner should be familiar with GeoGebra interface.
00:38 If not for relevant GeoGebra tutorials, please visit our website.
00:44 Let us begin our demonstration.
00:47 I have already opened the GeoGebra interface.
00:51 For this tutorial, I will first uncheck the Axes.
00:55 To do that, right-click on Graphics view.

The Graphics menu opens.

01:01 Click on the Axes check-box.
01:04 I will increase the font size for better view.
01:08 Go to Options menu, navigate to Font Size.
01:13 From the sub-menu, select 18 pt radio button.
01:17 Now let us construct a parallelogram.
01:20 Click on the Segment with Given Length tool.
01:24 Click on the Graphics view.
01:27 The Segment with Given Length text box opens.
01:31 In the Length field, type 5 and click on OK button.
01:37 Segment AB with length 5 cm and labelled as f, is drawn.
01:44 Let us delete the point that was drawn mistakenly.
01:48 This point may not be required for the actual drawing.
01:52 Right-click on the point. From the sub-menu, select the Delete option.
01:59 Next click on the Parallel Line tool.
02:02 Click below line AB to draw point C then click on line AB.
02:09 A parallel line to segment AB passing through C, is drawn.
02:14 Using Segment tool, join the points A and C.
02:21 Click again on Parallel Line tool, click on segment AC and then click on point B.
02:31 Two parallel lines g and i intersect at a point.
02:36 Click on Intersect tool and click on the point of intersection as D.
02:43 Now using the Segment tool, join the points, C, D and D, B.
02:53 Parallelogram ABDC is now complete.
02:57 We will hide the lines g and i, so that we can see the parallelogram clearly.
03:04 Right-click on line g, from the submenu click on Show Object check-box.

Similarly I will hide the line i.

03:15 Now we will explore the properties of parallelogram ABDC.
03:20 From the Algebra view, we can find that,

segments f and j are equal and segments h and k are equal.

03:31 Observe that, the opposite sides are parallel and equal.
03:36 Let us now measure the angles of the parallelogram.
03:40 Click on Angle tool.

Click on the points D C A

03:50 C A B
03:55 A B D
04:01 B D C.
04:07 Observe that the opposite angles are equal.
04:11 Now we will convert the parallelogram ABDC to a rectangle.
04:16 Click on Move tool.

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

04:25 Drag the labels to see them clearly.
04:30 Observe that all the angles changed to 90 degrees.
04:34 Now let us learn to construct a kite.
04:37 For this I will open a new GeoGebra window.
04:41 Click on File and select New Window.
04:46 To contruct a kite, we will draw two circles that intersect at two points.
04:52 Click on Circle with Centre through point tool.
04:55 Then click on Graphics view.
04:58 Point A is drawn, this is the centre of the circle.
05:03 Click again at some distance from point A.
05:07 Point B appears.

This completes the circle c.

05:13 Similarly, we will draw another circle with centre C and passing through D.
05:21 Notice that the two circles c and d intersect at two points.
05:26 Click on Intersect tool and click on the circles c and d.
05:33 E and F are the intersection points of the circles.
05:37 Now let us draw the required quadrilateral using these circles.
05:42 Click on Polygon tool.
05:44 Click on the points A, E, C, F and A again to complete the quadrilateral.
05:57 Notice in the Algebra View that two pairs of adjacent sides are equal.

The drawn quadrilateral is a kite.

06:06 Pause the tutorial and do this assignment.
06:10 Measure the angles of the kite and check what happens.
06:14 Draw diagonals and locate the intersection point of the diagonals.
06:19 Measure the angle at the intersection of the diagonals.
06:23 Check if diagonals bisect each other.
06:27 Your completed assignment should look like this.
06:32 To delete all the objects, press Ctrl + A and then press Delete key on the Key board.
06:40 Now let us construct a rhombus.
06:43 Click on Segment with Given Length tool.

Click on the Graphics view.

06:49 Segment with Given Length text box opens.
06:53 In the Length field, type 4 and click on OK button.

A segment with 4 units is drawn.

07:03 Let us construct a circle with center A and passing through B.
07:08 Click on Circle with Centre through Point tool.
07:11 Click on points A and B to complete the circle.
07:17 Using Point tool, mark a point C on the circumference of the circle.
07:23 Click on Segment tool and then click on points A and C.
07:29 This will join the points A and C.
07:32 Click on the Parallel line tool and click on the line AB and then on point C.
07:41 We see a line parallel to AB passing through C.
07:46 Similarly, draw a parallel line to segment AC passing through B.
07:53 Notice that the lines i and h intersect at a point.
07:58 Using Intersect tool, we will mark the point of intersection as D.
08:05 Using the Segment tool, join the points A, D and B, C.
08:13 A quadrilateral ABDC with diagonals AD and BC is drawn.
08:19 The diagonals intersect at a point.

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

08:30 Pause the tutorial and do this assignment.
08:34 Check if the diagonals of the quadrilateral ABDC bisect each other.
08:40 Also check if the diagonals are perpendicular bisectors.
08:45 Your completed assignment should look like this.
08:49 Now let us construct a cyclic quadrilateral.
08:53 For this, let us open Graphics 2 view.
08:57 Go to View menu and select Graphics 2 check box.
09:03 Graphics 2 view window opens, next to existing Graphics view.
09:08 Drag the border of the existing Graphics view, to see Graphics 2 view.
09:13 Now select Regular Polygon tool.

Click twice on Graphics 2 view.

09:20 The Regular Polygon text box opens with default value 4.
09:25 Click on the OK button.
09:28 A square FGHI is drawn in Graphics 2 view.
09:33 Let's construct perpendicular bisectors to segments FG and GH.
09:39 Select the Perpendicular Bisector tool from the tool bar.
09:43 Click on the points F, Gand G, H.
09:50 Observe that the perpendicular bisectors intersect at a point.
09:55 Using Intersect tool we will mark this point as J.
10:01 Now, Let's construct a circle with centre as J and passing through F.
10:07 Click on the Circle with center through Point tool, click on point J.

Then click on point F.

10:16 A cyclic quadrilateral FGHI is drawn.
10:21 Now we will display its area.
10:24 From the Angle tool drop down, click on the Area tool.
10:28 Then click on the quadrilateral FGHI to display its area.
10:35 As an assignment,

Draw a trapezium

10:40 Measure its perimeter and area.
10:44 Your completed assignment should look like this.
10:49 Let us summarise what we have learnt.
10:52 In this tutorial we have learnt, To construct quadrilaterals and understand the properties of quadrilaterals using GeoGebra.
11:03 The video at the following link summarises the Spoken Tutorial project.

Please download and watch it.

11:11 The Spoken Tutorial Project team conducts workshops using spoken tutorials and gives certificates.

For more details, please write to us.

11:21 Please post your questions in this forum.
11:25 Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

11:36 This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.

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