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